There definately are too many people on each country to put it down to one 'stereotype' but from what I've noticed:
Bishops: Are generally far more 'friendly' guys in that there is a lot more range banter (sometimes very frustrating, but usually a good thing) and far more Country channel nonsense (in a good way).
Bish seem to be great a packing together and organising big hits on bases and also seem to be willing to up and up and up and up again to kill troops or whatever.
I definately agree with the generally lower skill level, which is perhaps why they work so well together on the real-estate side of things... because they're not busy looking for good 1v1s (Of course this is not the case for all)
In summary, the Bish are great fun to fly with and good for the land-grabbing style of play (this is not a bad thing, just a different game aspect)
Rooks: Not as talkative on range or country channel but do communicate far more effectively in multiple-con situations... far better check-six calls and much more willingness (and competence) to help finish a rope or clear your six etc. (not to say that there aren't bish that do this, just not as many)
Perhaps as a result of this ^ the Rooks are, on the whole, far more accomplished fighter pilots (again, there are of course many great sticks on both other sides, i'm not trying to suggest otherwise)
I think that there are more tight-nit squads flying for the rooks, so I suspect that much of the banter on range that is found on the Bish side is done on closed Squad channels.
Rooks definately seem more interested in finding a good fight rather than taking a base (as I am, fighter combat is more entertaining for me), which is, again, just a different style of play.
As has been said before, those who fly a certain way will join with others who do the same (mostly, at least). So those who recieve no interest from Rooks in taking bases will see bases being porked and steamrolled by the Bish and think "chit, I want to be in that" and will head over that way.... because lets face it, everyone likes to win at least some times
Same with fighter pilots who tire of sloppy team-work... they see others doing it effectively and join them....
Knights: I've not flown with enough to make judgement, but they seem to be somewhere in the middle of the Bish and the Rooks. The jacks of all trades, so to speak.
This is how it seems to be during off-peak, Australian times.
The best thing anyone can do is take the time to switch teams for a good length of time, you make new friends, get away from the knobs on the previous country
:, meet new ones and learn new things.
It's always good fighting against those you used to fly with, too.