My age is showing here, but what about the old Infocom games?
The overall gameplay was about as linear as it gets (ask anyone who tried to get the Babel Fish in the Hitchhiker's game), yet the player almost always felt that they had complete autonomy within the game world.
I think it depends on whether you notice that your choices don't effect much. If the pseudo-choices are set up in such a way that you don't notice then I think the two are equally satisfying for those who like choice. That said, if it's really clear that the choices you're making are not real choices then I can see how that would actually not satisfy anybody - either the people who prefer linear experiences or the ones who prefer choice.
I mentioned on the Feeling of Agency topic about this The Legend of Zelda: Skyward Sword example, where the choice I had to make ultimately didn't matter, since regardless of what I did, I was going to get the same thing in the end. Thing is, even though this is the Illusion of Choice, I was still invested enough in the characters in the game to care about how I was going to go about that choice. Of course, not everyone would be as invested, so I figure this is a case-by-case thing. All-in-all, it's not about the choice, it's about how the choice is perceived by your audience.