Player Agency is when as a player, your decisions matter… they have weight and consequences, and play out into the future in the game. Narrative Control is when the player can control what goes on in the world, including what the consequences are or whether to accept them.
As I view them, they are incompatible despite the fact that at first glance they’re both about allowing the players to have input. The problem is that the kinds of input cancel each other out. Weighing the decision whether the character should do X or Y in the game hoping for consequence A or B becomes pointless as soon as you can control whether it’s A, B, or something else. And if you’re controlling the consequences, whether creating it from whole cloth or picking from a list, any time spent on the decision that led to that point is a waste…you’re just slowing the game down by pretending to consider probabilities and chains of causation which in the end will actually be decided by you choosing the one you like (understanding that like might mean what you feel is dramatically satisfying and not necessarily what the character would choose).
Now, if you’re very careful and aware of the distinction it may be possible to have a game where you shift back and forth…only having narrative control over things that aren’t the consequences of the decisions you’re making, and only pondering and planning out your decisions in areas that have been placed beyond your narrative control. That’s actually kind of how SFX! games work: players have a lot of narrative control over details of the environment, but only as long as they don’t really matter. If you’re in a bar and want to hit somebody with a bar stool, that’s mechanically the same as hitting with your fists, or a chair, or a bottle so you have narrative control over whether there are suitable bar stools in the place. It matters only insofar as hitting them with a stool might insulate you from their electric shock power, say. On the other hand, whether hitting them is actually going to hurt them is completely out of your control and in the hands of the GM and the dice, so the decision you are making to try to hit them instead of any of the other things you might attempt (grab them, knock the gun out of their hand, distract them by throwing a drink in their face, run away, etc) is an important one that bears assessing and reasoning about the probable consequences.
This is why as a player I have very little interest in games that emphasize giving the players a lot of narrative control: it’s something that actively interferes with my favorite part of RPGs. I want a lot of player agency, but only narrative control in very limited circumstances, such as when creating a character, or perhaps between sessions deciding what’s been going on in the character’s life off-screen.