You get near enough every type of clique in every school; I'll concede that the cliques in private schools are probably a bit more pronounced, but I'd say that's more down to the parenting rather than the schools.
I pretty much owe my school everything for what they did for me; I wasn't a confident child, and due to home circumstances I didn't really feel like I fitted in at a private school. Couple the home circumstances and the fact I got there on a bursary, I didn't mix in at first. The teaching style and the way they encouraged me to participate was brilliant though; it definitely helped me as a person.
I know I can't say this for certain, but if I went to another school I wouldn't be half the person I am today.