Hitman was a fps, where you were an assassin. The game, in my opinion, was really good, although it had some pretty strong flaws that probably dissapointed a lot of people. The missions were very open-ended, you were given a target and could do what ever you liked (snipe from a roof, disguise yourself as a waiter and kill the target at the restaraunt, etc.)
The problem with the original is that it became very difficult, very fast. Instead of being able to try one of a hundred possiblities, you had to find the one possibility that actually worked. The game also had some pretty goofy controls (which could be changed to something more familiar to fps fans). The game also had a 3rd person mode (the sequel is intended to be played 3rd person). There was a huge emphasis on planning, strategy, and stealth. Damage was fairly realisitc, so you couldn't take on an entire army by just charging and shooting (and there was a point were you had to go up against an entire army.)
Personally, I liked the game, it was challenging, and pretty unique compared to most of the other games out at the time. But it was very, very hard. Towards the end, it was getting kind of rediculous, it was so unfair. But I liked it anyway.
The sequel has better graphics, in-game saves, and claims to have better AI. That means that the AI will become suspicious of you if you do something strange, even while disguised. For example, in the demo for hitman 2, if you walked right behind someone for a long time (with the intention of strangling them) they'd keep looking back at you, and eventually open fire when they decided completely bald men with bar-code tattoos shouldn't follow that close.
I haven't played the sequel yet (just the demo), but I'm hoping its a good improvement on the original.