The end result is often an either/or, but the holy grail is that you'd get at least some of both: a strong narrative that is still a strong narrative even after accommodating a wide range of freedom of the player, whose actions meaningfully influence the narrative. You probably need some better AI to do some runtime story management, though, since as you point out, choose-your-own-adventure style isn't too satisfying. Sort of the computer version of what happens in RL roleplaying games with a good DM--- they keep the story on track, but incorporate a wide range of player actions into the story, so there's both strong narrative and player freedom.
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The end result is often an either/or, but the holy grail is that you'd get at least some of both: a strong narrative that is still a strong narrative even after accommodating a wide range of freedom of the player, whose actions meaningfully influence the narrative. You probably need some better AI to do some runtime story management, though, since as you point out, choose-your-own-adventure style isn't too satisfying. Sort of the computer version of what happens in RL roleplaying games with a good DM--- they keep the story on track, but incorporate a wide range of player actions into the story, so there's both strong narrative and player freedom.