Bioshock 1 :
Story and world building - good world building, as you progressively learn more about the characters, the story behind them etc.. that's one of the major reason of the progression as the game has a lot of boring gameplay unfortunately, some nice surprise through the story unfolding.
Design - sadly after a great start that get the underwater Rapture atmosphere right, the environment start to become boring, you'll see that it sadly and quickly become generic warehouse-looking after warehouse-looking rooms that lose completely the whole "it's an underwater city" atmosphere.
Missions - some parts are really good (like the Sander Cohen chapter) other are average or frankly not good (don't remember the name of the area, but there was one with lots of backtracking all over very generic areas with mobs always respawning)
Gameplay - it was bad to me because the whole environment is designed like a realistic place but your movements are 100% quake-like : some arcade sprinting lunatic all the time, with no variation of gameplay (out of the plasmid powers of course that at least made it fun).
Ending - i only got the good ending : i felt it was a fitting and very good one, very satisfying ending to the story, worth taking all that time saving little sisters. That was the best ending of all the Bioshocks that followed.
Bioshock 2 :
Story and world building - world building is also very good, taking place after the Bioshock events it completes a bit the world building of the first one and that focus on being a "big daddy" made you really interested in learning more about what's happening.
Design - after Bioshock 1 i got very surprised by this very good world design from the beginning to the end, unlike Bioshock 1 you never lose the "it's an underwater city" atmosphere, it's just brillantly designed.
Missions - i never felt bored by any of the game areas, the missions aren't a repeat of each other and you feel involved all the time, despite the respawning mobs it never get too repetitive.
Gameplay - not very good, the quake-like "out of place" feeling is still there, but it felt less pronounced than in Bioshock 1, and you don't feel like a heavy behemoth (like a big daddy was when you walk near them) out of when you jump and there's a very loud noise as expected when landing, at least the underwater sections change the pace a bit.
Ending - i only got the good ending : didn't liked it much, it simply did not felt rewarding enough (the worst evil of the game is "forgiven" with 0 comeuppance), your character die (at least in some logical way due to his body being designed for the sea depths huge pressure) at least his "daughter" and the little sisters you saved get to live.
Bioshock Infinite
Story and world building - world building is also very good in itself, everything feels right in the atmosphere the game is going for, there's no link to Bioshock 1 or 2 too, now the story i just disliked it with ever more one dimensional and cartoony characterisations.
Design - simply amazing , the city in the sky atmosphere is incredibly well done, the sense of majesty of the location is way above the 2 previous Bioshock, amazing work everywhere you run into.
Missions - they're good, there are a few areas in which you feel things are repeating too much, but overall you're always feeling involved though sometime the repetition of some fights in just different setup can (and will) be annoying.
Gameplay - it's much better, because the gameplay completely embrace the city in the sky setup, there's a lot of air pursuits and moves through cables all around the place, giving an alternative vertical gameplay to the default one.
Ending - there's no alternate ending and to me it's one of the worst Bioshock ending, not only it made very few sense once you start thinking about it, but it made me feel i so completely wasted my time playing while witnessing my character evolution from that piece of shit into that concerned father risking all for his "daughter" ...
Bioshock Infinite Burial at Sea DLC part1&2 (must play as it actually conclude the whole story)
Story - you're thrown on pre-Bioshock 1 Rapture, it's quite nice to see how it was before everything went to hell as you visit a bunch of place before their fall. But man, the storyline what the frack is that crap (see #1)
Design - part1 has some nice areas, the underwater feeling is average but far from as good as in Bioshock 2, part2 lose it completely and it never felt underwater anymore to me, quite similar to the 2nd half of Bioshock 1
Missions - the part1 start is stupid, you see grown up Elizabeth doing an out of character slutty femme fatale impersonation as if it was some old classic "film noir", but the game does not feel "film noir" once you're past the opening area unfortunately. The missions are only average past the start. Part2 has more originality thanks to its specific gameplay
Gameplay - Part1 is more of the same as Bioshock Infinite but with less verticality (there are a couple of areas with some) and Part 2 is completely genius, changing completely the gameplay into a stealth based game that is actually very interesting (and no other Bioshock did that)
Ending - Part 1 has a small surprise in its ending, nothing satisfying tough, Part 2.. probably the worst thing ever, the idiocy and nonsensical explanation of it is simply beyond words, what a way to kill Elizabeth and force a link to Bioshock 1 that never needed that game for that.
As a summary
Story : best is Bioshock 2 , Bioshock 1 is very good and worst is WTF Bioshock Infinite+Burial at Sea
Design : Bioshock Infinite is absolutely treasure for the eye, Bioshock 2 is amazing, worst is Bioshock 1
Missions : best are Bioshock 2 and Bioshock Infinite, Bioshock 1 is only servicable
Gameplay : best is Bioshock Infinite, worst is Bioshock 1
Ending : Best is Bioshock 1, worst is Bioshock Infinite and worst of the worst is Burial at Sea part 2
#1 super spoilery crap :
Burial at the Sea part 2 main story :
Elizabeth "oh i've been killed but i'm alive after all the story is a complete mess so whatever"
later
Elizabeth "got captured by very bad guy that wants to kill me because he's just very bad"
later
Elizabeth "i'm tricking that bad guy to get some time, but i'll 100% work for him"
later
Elizabeth "that guy is really bad and is totally not trustable but i'll do what he said all the time"
later
Elizabeth "i know he's going to betray me 100% but let's continue to do what he wants"
later
Elizabeth "he's going to sure kill me but i will have a plan"
later
Elizabeth "he's obviously lying, but he's not going to see me coming with my plan"
later
Elizabeth "i'll strike first because there's no way he'll honor his words"
later
Elizabeth "hey bad guy, we're in the endgame now, i'm here !"
*Elizabeth head is bludgeonned and caved in by bad guy
Elizabeth "that was how it should have been, let's sing La vie en rose"