I was in state education until I went to university and was lucky, my schools and 6th form college were excellent and I was also a hard worker and bright.
My boyfriend, at the time, and his brother went to a private school. I fared better at the exams etc. than they did (to be fair, they didn't work THAT hard) and I never felt that they had more academic advantages, or that the curriculum they were taught was more advanced, or that facilities were much better.
HOWEVER
What I did realise was that the school they went to, and the people they met their (well, the connections they made) potentially opened a lot of doors for them in later life. Not in a sleazy way, necessarily, but they were mixing with politicians' children for example, or heads of large companies.
I would always consider sending my child to a state school, but I do think life can be slightly easier (generalisation, I know) once you get to university and beyond, if you've had exposure to a private school education.