Is it? Explain the difference.
The difference between a general combat option and granting agency to a player via a resource is pretty significant. Obviously, one component of it is relative exclusivity. Choosing to do something anyone could have done is not that big a deal. Another is how it's resolved. Improvisation, for instance, is a very poor source of player agency, because it's really all in the DM's court, and 5e all but defaults to that, being very DM-empowering. A standard combat option (I'm trying to think of one other than attack) has more agency, since the player can probably expect the basic rules to be followed, though, again, anyone could have done it & anything unique/interesting that might happen as a result is probably up to the DM. A resource with explicit effects, like using a slot to cast fireball, OTOH, is higher-agency: it's dramatic, it's not something just anyone could have done, and it's a meaningful choice to use it or not, because it's a resource that must be managed.
If a class can perform a general combat option in a much superior fashion to another character, is that not a class feature/power?
If you take that far enough, sure. If you have a +2 to all your untrained jump checks, there's not really any agency, for instance. If you get a much larger bonus, and can exceed the normal maximums under the rules (jump more than your speed for instance), or jump on an entirely different scale than normal (like 30' straight up), you've got some more agency, because your presence brings an option to the table that other characters' presumably don't, but, since you can do it any time, it's mostly just your presence that changes the story, not your decisions. If there's a resource involved to do it, especially one that also has alternate uses, then that's even more agency, since your decisions of when and how to use the resource can make a huge difference to the story. So, even though one version of the ability might be 'more powerful,' because it's always available and does the exact same thing, it actually represents less agency, since you'll just always use it when it's applicable - a 'no brainer' decision is a less dramatic decision.
What is the difference between {two abilities similar} in terms of damage and effect {just re-skinned}? How does this provide any more differentiation and agency than the a {combat option} or feat?
Two classes having the same ability doesn't necessarily eliminate agency. For instance, the Druid, Cleric, and Bard can all cast Cure Wounds - it's the exact same spell, just re-skinned as divine prayer, nature magic, or arcane song - yet, if the party has only one of those classes, it's essentially unique to the character. Even if all three are present, the limited resources of each are still managed separately by the player, giving them some control over how things play out (each makes decisions: do you use slots for other spells, reserve them for healing, do you cure an ally who's low so he stays up, or wait for him to drop so the 'extra' damage inflicted by the enemy is 'wasted' as he heals up from zero, at the cost of him needing to stand on his turn, etc). The decisions of those characters make a real difference in how the game plays out. In contrast, the Champion Fighter might use this or that combat option (though there aren't many) or choose a feat that lets him do even more damage, but his choices are few and simple, and his contribution varies the most based on die rolls (crits, cold streaks or whatever), not those decisions).
The DM has to account for any overpowered combination including martial concepts.
Absolutely. Martial characters might churn out huge DPR, for instance. Locking them down so they can't attack, or giving the monsters outrageous hps or AC or resistance or immunity to weapons can compensate. That's fairly simple. The range of 'broken' things a 'Tier 1' caster can potentially do, OTOH, requires much more involved schemes to counter.
So don't pretend only casters created problems for DMs.
Tier 4-6 characters certainly presented the DM with challenges, too. Not just in trying to integrate them into the campaign in meaningful ways, but because even a lowly class could be optimized to do one thing to the point of being broken. Between needing to coddle most builds of an inferior class, and clamp down on the few abusive optimized examples, the DM certainly had a problem. Tier 1-2 classes presented a different set of problems, as they didn't even need to be intentionally optimized to be game-breaking, a well-meaning player could scuttle a campaign by accident, if the DM wasn't careful. The more imbalanced the game, the more headaches from the DM. It's easy to think that only the classes that 'broke high' were the offenders, but, really, any imbalance, high or low, could be a real problem.
It is, though, something most who have played D&D for a long time have learned to cope with one way or another. DMs can constrain overpowered characters, uplift underpowered ones, and keep the campaign varied and suprising to provide roving spot-light 'balance.' Players can build to concept, can eschew poor choices and even optimize, or collectively aim for the same general power levels with each of their builds.
All of those strategies still work in 5e.
Explain how they don't have narrative control? They decide how they defeat the challenges in their path. There wouldn't even be a narrative if they didn't have narrative control with their ability to defeat obstacles. The entire narrative is driven by their actions.
If your decision on 'how to defeat a challenge' is to hit it, or not hit it, you'll obviously choose hit it almost every time. That's participating in the story, but not having much agency in it. You could essentially go on strike and refuse to do anything useful, but you can't make meaningful decisions. If the DM puts in multiple enemies in each encounter, with each being more than just a clone of the others, or, at least, being positioned or armed differently or /something/ like that, then, at least, the order in which you choose to attack them might make some difference to that one scene. Now, if the DM gives you a few magical arrows of slaying that kill with a single hit, then the decision of whether you attack & whom you attack (with those few arrows) becomes a lot more meaningful. So, no matter how benighted the character, the DM can always build some opportunities for player influence into the narrative - ultimately, that's the DM exercising narrative control, but the player should at least /feel/ like he's sharing in it.
In contrast, a character given well-defined resources by the system gives his player some narrative control, in that how he chooses to use those resources will likely matter, and the choice can be made with some confidence, since he knows how they're usually supposed to work. Of course, just as the DM can create opportunities for the low-agency character to exercise some influence, the DM can block or neutralize the higher-agency character.
