I went to a run of the mill state school, and got 9 A*s, 1 A and 1 B. Its actually a really average/bad school, with some of the worst results in our area.
To be honest, I reckon it depends on the individual and how hard they work. Kids at private schools could have better teaching, more tuition and better opportunities, but they might choose to do nothing with it. Kids at state schools might have none of that, but work extremely hard to get to where they are now.
But generally, if a student does well, it means that they worked hard wherever they went.
Oh and public schools are actually more expensive private schools....places like Eton, where the royal family go. State schools are the normal schools that accept everybody. Just so you know lol!