I agree with you saying that Halo 1 is good, I personally think it is awesome. Anyways, about Halo 2 V.S. Halo 3, For 1 I have played many matches not being host and I have won/lost, even as host I have won/lost, and it's not because the host has an advantage. in fact the only time I've actually been killed because of lag was when I was playing a match with 16 people.
In my opinion I think the Halo 2 Campaign kinda sucks. And I'm pretty sure you can't beat Halo 3 Campaign levels in a "few minutes." The "slow, stupid" enemies actually a challenge. The cutscenes are the best I have seen In all Halo games. The equipment makes multiplayer/campaign more fun because you must be ready for anything. Also Forge is a great thing in Halo 3 not only because you can play it online, but also because some really good map varients have come from it. I'm pretty sure that there are no race/puzzle/infection maps on Halo 2. The fact of 4 player ONLINE co-op campaign on Halo 3 makes it even more fun especially when your friend snipes a brute chieftan in the head that was just about to smash you with a gravity hammer. Also A big problem I find in Halo 1/Halo 2 is the fact that splash damage is not present. I'm pretty sure a grenade does not affect the people on the other side of a titanium steel wall. Halo 3 also has better physics, pretty much everything in Halo 3 can be affected by physics except for the map structure itself of course. In fact, you can shoot a rocket coming at you with a sniper in Halo 3 and it will explode. In Halo 3 you can ricochet sniper rifle and Fuel Rod Gun bullets. And you can make rockets fly out of control with the gravity hammer.
Please elaborate on the bugs/problems/limitations.