From my observations so far in the early-mid game (I finished up to mission 4 in high chaos, mission 2 in low chaos, watched some different streams / videos up to mission 4) :
A large part of the dialogs stay the same, but some dialogs change (dialogs during cutscenes, notably with the Outsider, and during mission intro / outro). For example the intro to the 4th mission ends with "Save one genius, cage the other" in low chaos, "Save one genius, kill the other" in high chaos.
Some events change and small parts of the levels change. For exemple in the second mission there is a small back alley with a patrolling overseer in low chaos which is infested by bloodflies and blocked off (with the overseer dead inside) in high chaos.
A few comments by the heart also change.
Changes happen as soon as the second mission. You don't need to wait for the end game to see a difference.
The game advertises this in a loading screen / tutorial thingy like the first game: more dead people leads to a bleaker world, more bloodflies and a darker ending.