One of the things that Irrational emphasized during our time with BioShock Infinite, and that they seemed particularly proud of this time around, was the fact that the story will no longer be told through found recordings. Those still exist (in the form of "voxophones" lying around Columbia), but for the most part you'll experience events as they happen rather than hearing about them after the fact like in the original BioShock.
That's because unlike Rapture, Columbia is alive. This city is not ruined (yet—shit goes down over the course of the game, of course). Luckily, we'll get to be present for this particular story, rather than playing a minor part after the fact.