My second run through Rapture is not as good as the first...
The story takes place almost a decade after the first game with you playing as one of the prototype Big Daddies. After Jack's (the original game's protagonist) trek through Rapture, a hole was left on the food chain, which was occupied by a woman named Sofia Lamb. She takes over and begins using older Little Sisters and turning them into Big Sisters: more athletic and limber Big Daddies. Most of the story I had to go reread on Wikipedia, as it was a forgettable story and not a very good game compared to the first one.
The new weapons are cooler and fun to use. I spent a lot of time setting traps with harpoon weapons with trip wires and machine gun turrets. Another good upgrade from the first game was that you could use plasmids and weapons at the same time. Things that I didn't like were the "protect the Little Sisters" missions where enemies came in in droves and you have to set traps and prevent them from harming the Little Sister as she harvests bodies. The Big Daddy experience was not as expected, as enemies are faster and sometimes stronger than you, which compared to how much damage a Big Daddy usually takes to take down seems off.
Bottom line: forgettable story, gameplay is not expanded as much, multiplayer was, like most games today, only for people who bought it as it came out (I didn't play it, so I can't talk about it), although it does bring upgrades to the core gameplay. Ultimately, the changes were not enough to make it a great game as the first. It is very difficult to follow such a good game without many expectations with an even better game (the exception being Batman: Arkham City).