AC2 is the ideal sequel - an improvement in every single aspect over its predecessor.
It's unfair to compare this game directly to the first Assasin's Creed, simply because this game is such a vast improvement over it. It's always unrealistic to ask for such improvement from any sequel, but this one successfully pulled it off.
The story is very cool, extremely interesting especially for history buffs such as myself, and features some plot elements which have the power to drive religious skeptics, again, such as myself, crazy (in a good way). The game has you technically playing as Desmond Miles from the first one, and for the vast majority of the game you control him controlling the actions of his ancestor, Ezio Auditore, tapped through memories in his DNA via the Animus. The Animus is a machine Desmond lies down on which, through discovering Ezio's memories can uncover very important knowledge regarding the existence of man.
Lucky for us, Ezio Auditore lives in beautiful Italy, and the graphics portray various cities beautifully. This may sound bizarre, but the tiles on many of the roofs are awe-inspiring! The buildings are all great-looking and the cities are well-designed to allow for thinking of detours on the fly as you are being pursued across the rooftops by your enemies.
Ezio's arsenal of weapons is fairly large, and includes poison, a sword, hidden blades, smoke bombs, and even a small pistol ahead of its time. Using these weapons strategically to take care of your enemies is very fun and satisfying.
Fairly early in the game, Ezio is introduced to a poorly-tended small city which he can improve by investing funds which can return funds to him gradually. For example, it will cost money to improve an art store, but you will earn more money as its income also increases in proportion to the funds injected into its renovation. The problem with this, also seen in Fable 2, is that once you do much of the upgrades earning money becomes far too easy. The achievements are too easy, too, but that's not a big deal at all.
Acquire this game, one way or another. Don't kill a person for it, though. Because then you might, you know, get sent to prison for murder. ANYWAY, I would definitely recommend this game to anybody.