First off the points that I really enjoyed:
I really felt that the way you could combine certain plasmids with each other was a nice touch, even though it was limited to a few combinations.
I also enjoyed the story, which was key to, because the history of Rapture was so deep and interesting in the first game that I wanted more. This story delivered in many ways. Primarily the way that the Big Daddies were connected to the Little Sisters and how the Big Sisters came about. I also liked to learn what happened in the past ten years after the first game, which was developed in a very slow build manner.
The things that I didn't care for too much:
I felt that the bad guys weren't as various as they were in the first game. It seemed like I fought the same kind most of the game, which was kind of a drag. I honestly don't recall this from the first game, but this time it seemed like there were only 4 different kinds.
I also felt that the guns were less accurate, and not as powerful as the first. I found myself having to shoot some of the lower tiered enemies way too many times.
On a side note some of the Plasmids were overpowered, such as the insect swarm, which once I got it, I used it to take care of most of the threats.
Overall, I liked the game. Not quite as good as the first, but it had it's own charms to it. I really liked the ending and how it sets it up for another one. I would give it a 4.5/5 and would recommend anyone at least play it.
The multi-player which was added this time I around, I never touched. So I don't know how that worked out for them. What I've read is that it was pretty fun.