Rapture welcomes you back with all the good parts of the original and a few improvements!
Bioshock II is definitely a worthy sequel. While the awe of Rapture is not what it was in the original, the atmosphere is just as good. Rapture has worn in the decade since the last time we saw it - which is done really well. The new areas of Rapture (that I've seen so far) are the same quality as the environments in the original.
The sound is what really gets me with the sequel. I think it's better than the original. From the crazy cat-calls from around Rapture and the clink and clank of your footsteps to the music throughout, Rapture sounds alive.
New Stuff/Improvements
While I did enjoy the old hacking mini-game, the new one is much more organic. The action doesn't stop while your hacking, so while at first the new system seems easy, just wait til you're surrounded by a bunch of angry splicers and see how easy it is NOT to trigger an alarm. I also like being able to hack from distance. You have a gun that you can shoot a hackable machine from a ways away, making it fun to ambush splicers with alarms and sercurity bots.
Fighting/Foes
I've only played about 2 hours of the single player campaign (so this review is a little preemptive) but right off the bat I was very excited about the Big Sister as a foe. Fast, strong, and creepy, they are set up to be difficult, but fun, battles.
Guarding the Little Sisters is frantic and pretty entertaining - like a really well done version of the last part of the original Bioshock. The enemies just keep coming and coming and, while not there yet, I could imagine the later installments of these battles could be almost overwhelming - in a good way.
Overall I am very impressed with Bioshock II so far, even though I haven't gotten very deep into the game. I'm usually pretty skeptical of sequels - especially following up a GREAT game - but this is definitely a worthy chapter in the Bioshock universe.