The introduction of BioShock to Xbox One's Backwards Compatibility program was something of a relief for me. While I know and understand that some have purchased BioShock: The Collection, I don't think that should rob owners of the original versions a chance to play their old copies on their new console just because they didn't want to pay full price for the same game again. At least with BioShock: The Collection, an argument can be made that by virtue of its enhanced performance and visuals, that it is (somewhat) a new game.
Fortunately, Xbox agrees, but it may also come as a pleasant surprise to owners of the original game, that your Xbox 360 copy of the original game will see some enhanced performance. BioShock manages to hit 60 FPS, albeit not consistently and holds a higher framerate overall. It still doesn't quite measure up the enhanced version that comes in The Collection, but the Xbox One is officially the best place to play your old copy. BioShock 2 also sees an improvement in performance, but it's a lot more minute than the original.
Even if you don't own a copy of BioShock on PS4, Xbox One, or PC, you could do a lot worse than playing the 360 version on your Xbox One.