Nintendo fans are annoying, in general, for being endlessly optimistic. Much due to our manchildness. Hope springs eternal, in stark defiance of the harsh realities of the world.
Sony fans are annoying for being more militaristic in their tactics. If you don't think Uncharted is GOTY then you have NO TASTE WHATSOEVER! KILLZONE 3 WILL ROCK THE HOUSE! *fills page with 250 megabytes of GIFs*
Nintendo fans USED to be militaristic but we just ran out of ammo. This mirrored Nintendo, which turned away from traditionally competing with the others with Wii and DS. I also think constantly being a gen behind hardware wise has humbled Nintendo fanboys somewhat, but it's a two edged sword because now all that we can do is constantly hope, which can sometimes be equally annoying.
The Nintendo fanboys are annoying because they tend to be delusional but I find them tolerable mainly because it comes through that in their heart of hearts they feel slightly embarrassed about rooting for the disney of videogames. The Wii turned into a fanboy's worst nightmare at a certain point.
Sony fans are the worst because they combine a sense of entitlement with a large segment of the games as art crowd, mixed with that strong dose of advocacy because they still can't believe that everybody doesn't own a playstation or think anything Sony tosses out is wonderful.
I don't have a strong characterization of MS fanboys but I'm sure someone more up on things would be able to characterize it. Early on it had a lot to do with overly bragging about how MS started the gen but I don't follow the fanboys enough now to know what it migrated over to in the following years. Anecdotally I tend to think there are far less of them on GAF than the other two for whatever reason.
Before I was banned the PC brigade was the fastest rising annoying clique going over there. But that's been a few years. I don't follow GAF enough anymore to know if that is still the case.