I think Bioshock Infinite just does certain things better than Bioshock, while Bioshock does other things better. I feel like Bioshock has the better and deeper combat system, while Infinite has the better and deeper story/characters. However I don't think there's anything wrong with the combat in BI, it's just not as complex as Bioshock. The sky rail was a really fun addition to the combat in BI though once you get the hang of it.

Gameplay: Bioshock
Setting: Infinite (just barely though, and only cause Rapture is more limited by its closed in spaces opposed to the open world of Columbia)
Story: Infinite (will undoubtedly go down as one of the best video game stories ever)
Characters: Infinite
Innovation: Bioshock (but Elizabeth is a big achievement in innovation where Infinite is concerned)
Replay value: Bioshock

So if you value gameplay above all else in a game I think Bioshock is the winner, whereas if you prefer presentation values (story, setting, characters) Infinite is the winner.

That was what a didn't like in BioShock 2... BioShock Infinite is like BioShock... you have a world to explore and the world stands open to you visite everyplane everytime.

How can the devs remove all the good thinks to make a sequel? Oh God.

I havent touched the second one yet but I plan on giving it another shot once school is over and I platinium infinite.  

Mildly yes. I find the stages just meld into one and the one dimentional combat doesn't help.

Well you haven't finished the game yet. You'll realize that the world is not one dimensional.  

I really enjoyed it. One of the best games in a while. The combat gets dull, and I think that it lacks a proper "boss". Other than that it was amazing.

Maybe in BI, but I don't BS1 was any more open than BS2. But I really don't remember that much about the first two games, but I don't think there was much of any exploration to be had. Maybe, BI does have a bit more exploration to offer, but the levels are so boring, and short, I can't think of a good reason to go back looking for anything. I got that Key and I sure as hell am not going to go look for what it opens - if I run into it along the way then fine.

OK, i'll be back,...in a few days.

BioShock all the places is opened to be explorer... you can go back to the first room every time... BioShock 2 is level based, one level per time, finish it then go to the next... you can never go back to previous levels.

BioShock permit you even near the last boss go back to the first level to make some misson you didn't or get some secret that needs a weapon or plasmid that you just found in the last level.

Yeap... BioShock have a better replay value.

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For me:

Gameplay: Bioshock
Setting: Bioshock - Infinite I think just doesn't capture the same fell and believability as Bioshock did. I laughed when Booker first used the Sky Hook when he said "it must be magnetic" lol. Yes Booker, because the shit is unbelievable what you're doing, lol.
Story: I haven't finised Infinite as yet so can't pass final judgement. Although, Bioshock's story was quite good, so Infinite has its work cut out for it.
Characters: Hell no. No way those bunch of Republican zombies are as good as Splicers, Little Sisters and Big Daddys, etc.
Innovation: Bioshock, definitely.
Replay value: I don't really replay games, but I assume in this day and age, Infinite will have a bit more replay value.

I think as of all the elements (Music, Graphics, etc) that make up a game, Gameplay is always King. So if Bioshock has better gameplay, which it does so far, then Bioshock IMO would be the better game.