When comparing Halo 3 to BioShock one has to consider the kind of market each game was intended to target. Sure, they're both action oriented first person shooters, and they're both highly polished refinements over the literal and figurative prequels respectively, but these are simply surface comparisons. Once you get down into the core design of the game is where the differences really start to rear their heads. The Halo series has always focused its attention on both the evidently less-than-straightforward gunplay and the immersive, yet relatively simple storyline, while the Shock series has emphasized scary atmospheres and an overwhelming sense of dread that seeps out of every zombified chunk of flesh and sparking control panel. The Shock series also places a high amount of emphasis on skill development. Because there's no such thing to speak of in Halo, the player doesn't really have to take much thought when going through the game past the tried and true, "see enemy, shoot enemy, dodge bullets" tactic that's second nature to gamers everywhere. Halo's story, while enjoyable, doesn't leave the player much to think about after the fact.
However, there's something to be said about the social commentary that BioShock has in the focal point of its plot, the point where you kill andy ryan. BioShock is definitely a more cerebral game than Halo 3 is, I'd compare it to watching a movie vs. reading a book. Where Halo 3 is more pleasing to the sensual gamer, BioShock is more pleasing to the philosophical gamer. While BioShock doesn't quite stack up to its predecessor in that respect, its core gameplay elements have been polished and refined to a mirror sheen, making what would otherwise seem a drastic attempt at stylistic gameplay highly enjoyable. BioShock's predecessors suffered a bit in that regard. Both games have their strengths and weaknesses, but in the end if you're looking for something that's deeper than just a sweet action game, you're going to want to reach for BioShock.