Bioshock: Infinite has absolutely nothing to do with any previous Bioshocks. Those were great games with somehow believable stories.
This one is quite infantile in more ways than one, with a silly storyline and way too much dialog trying to explain it. The psycho-religious start with a forced baptism in order to be able to get in and play the game is sick to say the least.
Weapons are good (only reason to keep playing). Graphics are fair at best.
Elizabeth could show more skin while keeping her decency, but she has a cute attitude.