The difference in lighting here is pretty stark. The lack of shadowing on the little sister, and have a look at the candles behind her.
I don't think this one needs any explanation.
This one is more evident in the video, but the shadow from the fan above is cast on the diving suits in the original, and accurately moves with the fan's rotation. No such shadow is cast in the remaster.
This one is from the DF analysis. The underwater sections in Bioshock 2 were some of the best looking parts of the game, why would you want to neuter it like that?