Bioshock: The Collection landed a few hours ago, which includes 1080p remastered versions of Bioshock and Bioshock 2. I dashed through the opening sequences of the old and new versions of both games to get some comparison screenshots. The change is definitely far more noticeable in Bioshock, especially since the remastered version features an expanded FOV toggle in the options menu (Bioshock 2 Remastered does not). Have a nose through the gallery above to see how the remastered versions of both games look. I've noted which shot each game comes from directly underneath.
Performance-wise, on my GeForce GTX 980 I got around 330 fps with the original Bioshock games, while that dipped to a paltry 200 fps with the remastered version. The only issue I noticed while playing (keep in mind, I didn't play a whole lot) is that after remapping a few keys (C to crouch, really?) in Bioshock Remastered, the menu suddenly showed controller prompts (I didn't have a controller plugged in) and wouldn't let me mouse-click on any options (though I could arrow through them and hit Enter to select). A restart fixed this.
Check out our post for minimum requirements and instructions on how to get Bioshock: The Collection if you already own the original games.