Advantages: Less lag. Also no firewall/router configuration needed, no port forwarding.
Peer still requires firewall/router and port forwarding.
The difference is that Impulse Reactor's NAT feature is taking care of all that automatically.
Well Warcraft is P2P based too and it works great. Ppl just put desired locations in game name. By the way is there customizable game name? Or just some easy list in lobby?

Warcraft 3 is client server not pure P2P. The person who creates the game is the server. Sins of a Solar Empire is also client/server.
The reason those games can be client server is because people won't notice the effects of lag as much.
Ever played a first person shooter and thought "for sure" that you has shot someone in the head and yet they didn't die? The answer is, on your screen you did shoot them on the head but on the server (because of lag) you didn't.
In Demigod, because so much of the game revolves around a single unit and very timing sensitive moves latency is extremely important. In Demigod, all the screens have to be in sync. If they weren't, a player playing the Rook might throw a boulder and the game would have to deal with a situation where (due to lag) the target unit had moved. Then the "server" would have to decide whether that boulder hit the player or not which could get very frustrating.
In peer-to-peer, when you throw that boulder, that player is broadcasting that to all players at once. In client server, when you throw the boulder, it goes to the server (host) first and then is broadcast to all the players. That adds the latency between the host and the other players to the equation.
The big downside, however, is that in peer-to-peer, everyone is the host. So that person who has said "I can't host games but I can join them" from the Warcraft 3 days or in Sins of a Solar Empire or whatever has to somehow be taken care of in order to play Demigod and that's where the fancy Impulse Reactor NAT stuff comes in. But it's extremely difficult to do in a game that might have 10 people in it.
The more people you try to connect together, the harder it gets (N^2 hard). A 5 on 5 game with random strangers is probably not a good idea. We've done it but it can take a long time for them to connect and most people won't have the patience to wait 45 seconds or so for a person to connect.
Based on the metric tests we've done, there is a 95% chance that two random players will be able to connect to each other. But the odds greatly decline as you add more players because there will be cases where two players just can't connect to each other for any number of technical reasons that can't be controlled by the software.