Bioshock 2 is an example of taking good ideas from a game that squandered them (Bioshock) and turning them into fun, meaningful mechanics with a complete and interesting weapons arsenal and even taking the halfbaked over-reliant on "moments" story of the original and turning it into something consistently interesting.
Bioshock 1 was plagued with mediocre level design in areas that were often all too similar to one another and could simply be described as hallways connected to cube rooms connected to stairways connected to hallways. Never did it branch from some very tired level design. The AI and enemy behavior never made itself out to be anything interesting, the best it got was big daddies who were at best side strafing, spamming tanks. Never anything elaborate once you do your damage dump into them.
Bioshock 2 turned everything from the original that was terrible (and there was a lot of it) in to something good, interesting, challenging, and requiring you to engage in the now interesting mechanics, make use of the good weapons, cut away the fat and make something good with what's left.
The arsenal deserves praise for avoiding the traps the original did, gone is the mediocre ensemble of standard first person shooter set, and in comes the bombastic drill, the meaty double barreled shotgun, the rivet gun and all the unique ammo types that helped differentiate each weapon just a little bit more.
The level design is full of interesting locales such as themeparks to the ocean floor which give the game a chance to show off rapture as more than just hallways and cubed out rooms. Some much needed fresh air there.
The story in the original people seem to forget is nothing without those little special moments. The Ryan speech, the would you kindly, the Cohen gallery, without those moments? It loses a lot of its edge. Between all of this its padded, boring, and nothing very peculiar or interesting really happens between those peaks in the story. It never managed to be consistent. The sequel once again fixes this, engaging the player in sporadic big sister fights, trailing them along with harvesting defense situations, it all worked very well.
Most people shat on the game for not having those big, bombastic speeches, but forgot those little special moments, like when you're working your way through the entertainment district to kill that hasbeen, only to have that chance to spare her. After you learn her story, it becomes a legitimate moral choice for the player. Do you take your revenge for all the shit she put you through, or understand her plight and realize she may make a better ally in the end? Things like this show the teams determination to unfuck all the failures of the original.
It's a little sad to see OP who can't piece these things together. Bioshock 2 is a more subtle game than the first, it's much less flamboyant, much less bombastic and in your face, but it's far more rewarding, better designed, better paced, and a better game ultimately. It didn't have a pretentious and deep story, because it didn't need it. It had a functional story that played with the game mechanics and designs decently, and it was more rewarding and fun as a focus. It's frankly the only game worth giving a damn about in the entire Bioshock franchise.