Halo 2 is really two games in one. The single-player campaign is very similar to Halo 1, and is completely underwhelming. The Multiplayer, on the other hand, is brilliantly put together and runs beautifully on Live.
Halo 2's campaign suffers from most of the shortcoming of the original. The levels aren't that interesting, and are extremely repetitive. You will often find yourself going through identical rooms for extended periods of time, fighting waves of the same enemy. There are also some extremely annoying enemies in the game. The weapons are OK, but other than the energy sword (which is great) don't represent a big improvement over the original.
The multiplayer setup is very fun. The netcode for H2 is brilliant, and it runs great even on my inferior 125K "DSL Lite." The gameplay options aren't very interesting, but the maps are generally good, and you won't find a better online FPS for consoles. Clans are supported, and can lead to some interesting team battles.
One major shortcoming in the multiplayer mode is that there are no bots in the game. Another is that you can't scroll through a list of games and join one. Instead, if you want to join a custom game you have to do it through your friends or clan members.
Overall, H2 is a good refinement of Halo, and the multiplayer component is great. If you have an XBox and Live, you have to own Halo 2.