It seems like Wii fans are generally retaliatory rather than offensive. When someone comes onto a forum with a "Wii is for babies and looks like crap!" line (it happens a LOT), then Wii fans defend it. But I don't think they go into other places looking for trouble or to insult just to start a flame war. I'm primarily a Wii player, so that's what I have the most experience with. In every Wii-only forum I'm in, about 1/3 of the posts are anti-Wii. I'm guessing it's becoz they're "ahead" right now, although I'm not sure why people consider it a competition between different consoles.
I still keep up to date on the other consoles though, and I actually had a 360 until very recently. But it seems like from what I've seen, the 360 fans are the most aggressive, trashing stuff like Killzone 2 simply becoz PS3 fans are hyped about it, then trashing Wii stuff becoz it's not HD and "looks so terrible". I know they're 360 fans becoz they always list Gears of War and other XBOX exclusives as their "proof" that the 360 is somehow better than everything else. I guess PS3 fans are too busy fighting with 360 fans to be worried about Wii fans maybe, so that's why I don't see them pop up in Wii forums as much. I dunno.
It will never end though, unfortunately.