Infinite.

I thought the first one was brilliant. Infinite, however, breaks boundaries and redifines a stale genre. It's THE game to play. Amazing from beginning to end.

Infinite had a great opening and great epilogue, but the gameplay and level design felt constrained.
2 had the best open level design and gameplay, loved exploring every bit of it.
The first one has great story, atmosphere, integrated gameplay mechanics, level design, only the ending was a bit lacking.

First one wins overall.

I would say Infinite.

Gameplay is about equal. But Infinite raised the bar on story and presentation.

Bioshock 1> infinite

Bioshock 1 was the best Infinite was the worst, Bioshock lost most of it's atmosphere when it left rapture.

Let's put BioShock 2 to one side immediately. It's not a bad game, but it lacks all of the originality of the other two, and has a far less interesting story.

It's very close between BioShock and BioShock Infinite. Both are certainly in my top five of the generation. Both have excellent narratives, a range of strong characters and varied and exciting gameplay. But I think Infinite just goes that little bit further. I prefer the Vigors to the plasmids, I liked the removal of EVE Hypos and medkits, and I loved the way Elizabeth was integrated into the game.

So, I think Infinite just about edges it out for me.

Okay, you can't just say this and run off. Why did you think 2 was better than Infinite?

Overall the gameplay was just so much better for part 2 than both the other games. Better weapon upgrades, better enemies, more plasmids and plasmid upgrades. I found infinites gameplay to be the worst by far. I just enjoyed part 2 alot more, i beat it like 4 times just to experiment with different weapon and plasmid sets while playing infinite a second time would just be for the story that i didnt even find to be interesting. 

Its like the devs for infinite didnt even play part 2 and if they did they went and said " Ok, bioshock 2 expands on the gameplay of part 1 dramatically with amazing upgrades and tight shooting mechanics. Lets just not do any of those and go with the same old mechanics". 

I can't really vote as I haven't played Infinite yet. (Really want to, but my brother has the 360 at the moment)

Out of the first two, I'll take Bioshock 1 by a landslide. In my view, it's the third best game of the 7th generation, outdone only by the Mario Galaxy games. The atmosphere, the combat, the story, simply amazing stuff.

The second one was a very good game, but it just didn't have the same creative spark.

Bioshock 1 followed by 2 and than Infinity. I had high hopes for Infinity, but I just didnt care for it too much.