Sure, OK, let's focus on this.
Just to make sure we are on the same page before I begin. These are "stories you can do with gods, but not archfiends"
For starters, gods generally don't show up on the prime (except during the Time of Troubles, when they were banished there). They send servitors. Archfiends can show up in person. This means you can literally has Orcus (or an aspect of Orcus) in your game without having the players plane shift. (Also, archfiends have stats, so they can be killed.) Sure, killing an archfiend on the Prime doesn't destroy it, but it prevents that fiend from reappearing on the Prime for a good long while, and that's just as sweet a victory. Demons and I believe devils both have soul-amulets, so if your high-level PCs felt really ambitious you could have adventures involving finding and destroying an archfiend's amulet and thus actually killing the archfiend.
Coming to the prime and being killed by adventurers is a story you can possibly tell with both evil gods and archfiends. This seems incredibly interchangeable so it doesn't fulfill the point.
Now, I can already feel your accusations, so let me clarify, again. I am not saying this is a bad idea. I'm not saying you are wrong that gods rarely come to the prime. I'm not saying this is a bad story. I'm not saying you must bow down before my "one true way" story. I'm saying, and only saying, that I could use an evil god in the exact same plot of coming to the mortal realms, of players hunting down an artifact needed to truly kill the god, and doing so. I could also tell the story of archfiends being completely unable to form upon this mortal coil. these stories are interchangeable. So they do not support your claim.
Gods have temples are are more widely accepted. Fiendish cults are usually kept hidden. Thus, stories involving gods will usually take place out in the open, while cults are going to be sneaky and understated. If the High Council are all worshipers of Iuz, they're all going to have his holy symbol around their neck and they are going to be openly evil, or at least fine with evil. If the High Council are all worshipers of Titivalus, they're going to keep that a secret. Finding out this secret and revealing it--and ensuring those you reveal it to aren't also worshipers of Titvalus--will be an adventure in and of itself.
If you have a city where worship of a particular evil god is outlawed (in Waterdeep, it's illegal to build temples to Talona), you can have a more political story where priests of that god are trying to get the religion accepted. The story can be, Waterdeep has suddenly reversed that decision and a temple to Talona is being built. Everyone wants to know why. It's up to you plucky adventurers to find out. It could be something as simple as bribes or something darker like mind control or even murder-and-replacement. But it's really hard to imagine this plot going on with worshipers of Geryon or Zuggtmoy.
No, again, these are easily interchangeable. I can easily imagine an evil god who is not widely worshipped, whose followers are secretive members of a cult and the adventure is about unveiling them. I've even got a DnD example in Vecna from Exandria and Critical Role.
Reversing that again to archfiends being openly and even proudly worshipped... I've actually done that in my campaign already. Do to some inter-party shenanigans, alliances between party members, and some major plot points, a potential future for my homebrew world involved elves openly worshiping the new Lady of the Fifth, The Fallen Huntress Tana. She offered them bloody vengeance against the mindflayers for horrific crimes against the elven people, and was friends with the party member who was basically an elven Arthur, rebuilding the empire and bringing it back to glory... and openly stating that they would allow legal worship of the devils.
So, again, secretive cult worship of an evil being, or open to the public worship of an evil being. I can do that with either Archfiends or Evil gods, so these are not stories that can only be told with one or the other.
With archfiends, you get into things such as soul contracts, which you don't have with gods. You can also make deals with archfiends for power, including various fiendish boons. Sure, by RAW, a PC can suddenly decide to take a level of cleric or warlock, but many DMs are going to require that the PCs justify that multiclassing in some way.
Sorry, I can easily picture an Evil God of contracts, who treats his worshippers in a Pax Romana style of transactional worship. I can only grab part of the article (I heard about this in a video) but to give this context from the Britannica "
Yet Roman religion was based not on divine grace but instead on mutual trust (fides) between god and man. The object of Roman religion was to secure the cooperation, benevolence, and “peace” of the gods (pax deorum)."
So, under this style of religion, a contract between man and god is expected.
Now, one adventure type both gods and archfiends will create is when the PC has to go on a quest for their power. The main difference is that with a god, the PC will be asked or commanded by the priest (or through a dream), while the archfiend may send an actual minion to do the "asking," if it doesn't show up in person.
This isn't a difference at all. There is no difference between a preist of a god or a cultist of a demon, and gods have sent angels plenty of times to give quests, so sending a fiend is the exact same.
Archfiends often try to pervert other religions (good, neutral, and evil ones alike), either making a mockery of the faith's beliefs or introducing fiendish influences. This means you can have adventures where you find out that a local religion is starting to turn to the dark side. Evil gods generally don't try to get their worshipers to pervert other religions in this way--they're more into forced conversions or outright killing the nonbelievers.
They don't typically, but is there any reason they can't? I can easily imagine an evil god attempting to spread their influence and weaken their rivals by putting their own influences and iconography into the worship of another god. And mocking other god's beliefs and practices is easily done as well. In a way, we do it all the time.
And, flipping it, I see no reason that Demonic Cultists can't do forced conversions or murder. They are pretty good at both, actually. So, again, I don't see this as a story that is impossible to tell with the opposite type of being. It isn't typical, I will give you that, but an atypical story doesn't mean it can't be done or that it can't be done well.
And, since I've gone through a few of these, I'll go ahead and clarify again. I'm not saying your ideas are bad. I'm not saying these ideas are wrong. I'm not trying to convert you to the "one true way". I'm not trying to "gotcha". I'm honestly looking at each of these examples and asking "is it possible for me to tell this story with the opposite type of being" and each time so far... yes, it is.
You can also introduce fun moral dilemmas such as, worshipers of Yeenoghu are corrupting a temple to Malar. Malar's priests are evil and chaotic, but also have something akin to a social structure and rules (they won't kill the young or pregnant), whereas Yeenoghu's worshipers will murder everyone and may also spread Yeenoghu's insanity (that's not RAW, but it's fairly reasonable to homebrew that idea, especially when MTF had a sidenote of a person mind-reading a gnoll and because of that, slowly going mad and becoming a cultist of Yeenoghu). Do you help the Malar worshipers, fight them both, or let them duke it out on their own and hope that their fight doesn't harm innocents?
Not sure if this is meant to be a seperate example but "lesser of two evils" is also possible to do with both Archfiends and with Gods. You don't need to pit them against each other to pull that off. Internal conflicts between the two can lead to the same story.
Gods are sort of part of the world. Even the evil ones are kind of necessary for the world to keep turning, in some way, because what they represent is already an aspect of the world. Sure, some of them are awful, but they're kind of awful in the way that things like parasites or forest fires are awful, but also useful in a way, even if it's not a way that most mortals can easily see.
But archfiends are more like cancer, doing horrible things to a world that they're not part of. Hyenas would just be animals if Yeenoghu hadn't turned them into nearly mindless and monstrously bloodthirsty gnolls. Fungi are needed to recycle dead things so that the living can continue to exist. Zuggtmoy's fungi are corruptions of this, turning a much-needed organism into monsters that do no good. Undead would likely be limited to what were created by mortal wizards or to ghosts of those who can't pass on if Orcus hasn't decided to start turning them into creatures that prey on the living.
What this means is that you can have plenty of adventures involving an archfiend's evilness affecting an area, and the PCs have to deal with it. While by RAW these are regional effects around the archfiend's lair, you can also use them as the after effects of their cults (a bit of the archfiend's power is imbued in the cult's altar, perhaps), especially if its a powerful one. 3x had the "Corrupted Creature" monster template for just such a event. But outside of the hallow spell, few people assume that anything unusual happens around a temple to a currently-worshiped god, even if the temple has artifacts in it or bits of dead saint or whatever. It's holy (or unholy) ground, but other than that, not too much happens beyond a few more or less undead.
So, you can easily tell a story where the gods are not a natural part of the world. Where they come from beyond our realm to play their games with us mortals like chess pieces and an evil god is disruptive and harmful to the very fabric of reality in the same way as your archfiend example. I've actually seen it done, though the name of the work escapes me at the moment.
You can also have it where the fiends ARE part of the natural order. Japanese Yokai embody this entirely. They are evil spirits, but they are a natural part of the world. A part of the world that desires to harm you, that enjoys harming you, but the world isn't a kind place.
In fact, one of your earlier ideas in this thread (I think it was you) inspired a dark gothic world in my head where the fiends are natural and the gods are unnatural, and the natural state of the world is one of darkness, blood and terror, and the unnatural gods are preventing this state of primal darkness.
So, once more, I find this unconvincing. I can do either story with either type of being.
And then, of course, there's the "the archfiend's cult is trying to turn their patron into a full god; you have to stop it."
Which has always been a bizarre story to me. I would have to admit though, the "archfiend is trying to become a god" story is one that can't be swapped like I've been doing...
Except, the larger archetype of the story is "powerful evil being is trying to become more powerful, and we must stop them". I bring this up, because the famous 2e Vecna three-part adventure involves Vecna (a god) tricking Iuz (a demigod/god) to entering his domain, so that he could consume his power and become an even greater and more terrifying god in his bid for the control of all of reality by conquering Sigil.
So, while I fully acknowledge that the specific story of "non-god being trying to become a god" isn't able to work without one side being a god and the other not, the larger trope of "evil power-up ritual we must stop" does still work with either case.
But hey, we got one.
Stepping off the Prime, there's the Blood War, which allows any number of war-based adventures: fighting in it, trying to prevent an arm of the War from affecting a particular place, aiding or hindering one side, and so forth. There's also fiendish coups, where you can prevent (or help) one archfiend from taking over another one's.
All of this can be done with Evil Gods. Endless war between Magbuliyet and Gruumsh is very similar in style to the Blood War. Coups can happen to gods. Happens pretty regularly in various fictions.
Petitioners in a god's domain want to be there, because the ultimate goal for a petitioner is to merge with the god's domain and therefore the god. The souls that an archfiend has almost certainly don't; in fact, they probably have souls that don't deserve to be in Hell or the Abyss. Adventurers can try rescue those souls. Archfiends also have more use for living beings than gods have (as minions, servitors, or slaves, mostly), who primarily use the living as proxies (as per Planescape). Thus, you can rescue living beings who are being held by or are working for archfiends.
Wow, a lot to unpack here.
Petionersin a god's domain want to be there? Okay. But they are an evil god right, so it is still terrible and likely torturous place. And Archfiends can have the same story. I actually had a player recently who was playing a Hell Knight, they wanted to go to the Nine Hells when they died, so they could become an eternal soldier fighting for the cause of proctecting (conquering) the multiverse. Many cultists want to go to the hells or abyss because they think they will come out on top, and they are often proven wrong... but there is no reason that same thing can't be true for an evil god's domain.
Souls that don't belong in the evil realm of the evil god/Archfiend? Yep, that story can and has been told with both types of beings. That is the entire trope behind unwilling human sacrifices after all. And adventurers can go to rescue from either place.
Also, I don't even agree with your final point. Gods also have a lot of use for living beings and use them as proxies all the time. And living beings can be held captive or in enforced servitude by evil gods or by archfiends. No difference in that story.
In addition to the Blood War, archfiends fight amongst each other for other reasons. These battles might spill out to other planes, including the Prime, and do so far more often than with god vs. god battles. The PCs can fight one or both fiends (and their cults) at the same time.
And "far more often" tells us that these stories can be told with either archfiends or Evil Gods. So, no difference here.
So, that enough possible plots?
These are all excellent plots. But all of them could be switched and told from the other side. So, again, to reiterate, the question asked was "What story can you tell with an Evil God that you cannot tell with an Archfiend?" and the only one you provided is an archfiend trying to become an evil god.
Again, I'm not saying these are bad plots. I'm not saying that they are terrible ideas. I'm not saying you are a bad person for having come up with them, or that there is a "one true way" to tell these stories. I'm saying that I can take every single one of these stories and make it work with the other type of being. Except, specifically, the "Archfiend trying to become an Evil God". Which, technically, I could do "Evil god tries to become an Archfiend" but due to the re-defining that would need to happen, it would likely not work out as well, and I am willing to concede that plot. All the others were interchangeable.