I went to public school and since that is all I know - I can't say if private would have been better for me. Public school didn't harm me, and I have to assume it benefited me. I had some great teachers and some that were not so great.
My kids went to private school for a few years until we moved. They learned great study habits during those first years that served them very well in their later school years. I liked the smaller class size in the private school. They learned some wonderful things that they might have missed if in a larger classroom if the teacher had less time.