I wouldn't change the fact that I went to non-selective state schools. I think that if you're bright, you'll get good grades no matter what, and if you research the schools in your area to see what they're like instead of just going to the closest one then sometimes they can be just as good as private schools. A lot of the parents of kids in my year who understood the system chose to go to the schools that were a couple of miles further away, because the school in their town was mediocre and had a **** environment.
I think if you're of average intelligence, in an average state school, you'll get average grades, but in a private school you'll get pretty good grades. If you're above average, you'll get very good grades in private school. If you're below average then by going to private school it's unlikely you'll get below average grades.
However, I think the private school evironment benefits students in ways other than grades. Many of the parents, students, and faculty will "know the system", and will teach others about how to be confident in certain situations. It removes a level of ambiguity and uncertainty regarding, e.g., university applications if you are made very aware of all the options available to you and are able to see the outcomes of all those options. I'm very lucky, because my parents taught me a lot about the education system and about what "matters" and what is fluff to get a good Ofsted report, but most people don't have that background and as such are at a disadvantage when it comes to applying for work experience, jobs, or university places.