There's nothing wrong with going to a public school if you really want to, but I'd probably go to a private one if I had the money. Mainly because private schools (in my town, at least,) have smaller class sizes, which I find to be fantastic. That, and the material being taught seems more to my liking than that of public schools.
As Aizuke stated, though, public schools seem to trump private schools when it comes to sociality. This is probably because you would have more diverse of a community around you, and more people to talk to. Not saying this is the case everywhere, but an observation based on experience.
Either way, you're getting something from the school, be it public or private. It all depends on how you feel about it.
