The Batman/Superman comparison is a lot more useful though, and is part of why it gets brought up so much. Batman IS, to a meaningful degree, meant to be one of Superman's peers. That's an intentional part of the storytelling. Further, Batman has several "powers" that Superman doesn't. Political and business connections, fear factor (few villains fear Superman, despite knowing his vast strength), vast fortunes that can be funneled to "black projects" without people noticing (seriously, the Watchtower was a hidden line-item in Wayne Enterprises' aerospace division budget!), and (depending on canon) greater intelligence and superior observational skills (sure, Superman has x-ray vision, but he overlooks stuff Batman wouldn't.) It's also at least implied that Batman is more resistant to mind-control and possibly magic, whereas magic is one of Superman's only weaknesses. And, narratively, they fill very similar roles in the story, rather than being radically different like Merlin and Arthur or Sam and Gandalf.
I wanted to take a moment to look at this, and point out a rather fundamental... flaw sounds wrong, an assumption, if you will.
Let us take Darkseid for a moment. Darkseid is not from Earth, has the resources of at minimum an entire planet, and is strong and fast enough to fight superman blow for blow.
Look at those "powers" you list for Batman.
- Darkseid doesn't fear Batman, that's ridiculous.
- Batman's political connections and business connections are rather meaningless in the face of an entity that conquers worlds with relative easy. What does getting the Mayor of Gotham to listen to you do when the war can obliterate gotham as a statistic?
- What does money do? Nothing much. What you would need is to put in weapons development. But, there is a fundamental problem here, what weapon that can be made by earthly hands can kill Darkseid? Guy is just as invulnerable as Superman, but he has no kryptonite.
- What use is observational skills against an enemy that doesn't care if you see him? Why would Darkseid even attempt to mind-control Batman? What value does that hold for him?
And I think this is a fundamental problem that doesn't get addressed very often. Batman cannot stop Darkseid. The absolute best he could do is have someone else build super tech that might give him a fighting chance. So, in an adventure focused around "stop Darkseid" there is nothing Batman can do other than distract the monstrous god of evil while Superman tries to punch him.
Now, take a moment to consider Zatana. Zatana isn't a magician, she is a reality-warper. Her spells can literally do anything, and she has fought things that erased all of existence. If she says "I have an orbital laser" she has an orbital laser. Batman has to leverage existing resources, he has to use money, he has to use connections. Zatana creates new resources. She runs into a problem and can come up, on the spot, with whatever tool or ability is needed to solve that problem.
So, if you have Superman, Zatana and Batman in a fight against Darkseid... Zatana can fight. She has to be careful, she has to be clever, but she can put up a fight... and is more effective than Batman. The only way Batman can contribute is if A) He has been secretly building an Anti-Darksied Plot Armor weapon or B) if he is given a DIFFERENT MISSION to accomplish. Which is fine if Batman's player is cool with it, but if he wanted to take down the BBEG... he can't. He just doesn't have anything that is applicable to the situation, and his best hope is being given a solo crafted side-mission, which can't be done by Supes or Zatana... because they need to keep fighting the real threat.
Batman gets plot armor all the time to stand up to the level superman is at, but the real show comes when you take some of the most iconic villains from both sides. Batman can't touch Darkseid or Doomsday or Mongul. Sure, he can fight some of the others, like Toyman or Lex Luthor, but there are a lot he cannot stand up against.
Is there a single iconic villain from Batman's gallery that would actually be a challenge for Supes? Joker sure isn't. Penguin, Mr. Freeze, Killer Croc, Clayface, Riddler, none of these villains could actually do anything to stop Superman. He'd destroy them in moments
Having powers others don't is only applicable if the situation allows for those powers to be used, and when faced with overwhelming power, you get very niche cases where specific types of power can be reasonably and consistently stacked up against each other.