Let me start by saying that if you enjoyed the first Bioshock game, then you'll definitely enjoy the sequel. But having played through this game in a couple of days, I wouldn't necessarily say that it is better than the first. Let me explain.
The best improvement is the new ability to dual wield both your weapons and plasmid powers at the same time. It was such a pain having to constantly swap during battle in the first game. It made gameplay unbalanced and made for a lot of tedious replaying when you selected the wrong plasmid or weapon to combat an enemy. This addition makes the combat engine more fluid. But don't expect the enemies to be a push over, as the amount of damage the Splicers can take has been raised to compensate.
I also like the new ability to set traps for the Splicers using special ammo in some of your various weapons. This can require some planning, and doesn't just involve bursting in and hoping for the best, especially when short on ammo or health. This… more »

Let me start by saying that if you enjoyed the first Bioshock game, then you'll definitely enjoy the sequel. But having played through this game in a couple of days, I wouldn't necessarily say that it is better than the first. Let me explain.
The best improvement is the new ability to dual wield both your weapons and plasmid powers at the same time. It was such a pain having to constantly swap during battle in the first game. It made gameplay unbalanced and made for a lot of tedious replaying when you selected the wrong plasmid or weapon to combat an enemy. This addition makes the combat engine more fluid. But don't expect the enemies to be a push over, as the amount of damage the Splicers can take has been raised to compensate.
I also like the new ability to set traps for the Splicers using special ammo in some of your various weapons. This can require some planning, and doesn't just involve bursting in and hoping for the best, especially when short on ammo or health. This is also a welcome extra.
I was probably most disappointed with the new Little Sister adoption ability. This sounded very promising on paper, but to me felt like it amounted to nothing more than a series of tedious mini-games. I assumed that the little sister would aid you in finding secrets etc, but instead is mainly the key to acquiring extra 'Adam', which is the currency for buying new abilities and powers. For every one you adopt, you must search the level looking for two corpses that contain 'Adam' and then defend the Little Sister against hoards of respawning enemies while she collects it. Sounds simple enough, but by about half way through the game I was bored with this method. It's always the same routine, and it can use up vast amounts of precious ammo and first aid kits. The thing is that you don't have to bother with this at all, and can harvest or heal the Little Sister straight away, but doing so will make it very difficult to progress without leveling up your abilities.
Believe it or not, I also felt that playing as a Big Daddy also spoiled the game a little. Everybody agrees that the new drill weapon is cool, but all the other weapons are merely just Big Daddy versions of the ones from the first game. Also, despite the amount of effort it takes you to kill a Big Daddy, in comparison you are a bit of a push-over and are just as feeble as Jack in the first game. Playing as just an ordinary guy in the first game also made the game a lot scarier, as you constantly felt vulnerable and out-numbered, a stranger out of his depth in a hellish nightmare. Playing as a Big Daddy takes this away, as you now feel more a part of Rapture, rather than an unwilling observer. Imagine playing Silent Hill as a space marine! Just wouldn't work.
My biggest gripe though is that yet again there is zero replay value. You spend hours leveling up, gaining new powers and upgrading weapons, only to have it all taken away at the end of the game. Yes you can up the difficulty, but apart from this the game offers nothing new the second time you play it. I hated this with the first game. I still had weapons to upgrade and plasmids to buy and master, but instead I had to start again from scratch. I really thought this would have been addressed for the sequel as although some may argue it makes the game too easy, it does give you a chance to master your gameplay skills.
Multiplayer is certainly a welcome addition, but can be mastered quickly. A lot of time has clearly been spent on this, which is why little has been added to the single player game. I suppose if it ain't broke don't fix it, but I couldn't help feeling I'd seen it all before. Still an excellent title while it lasts, but not quite the leap foward I was expecting.