I went from a state primary to private secondary school when I was ten, but I think that's a bit early for it to matter - I'd never even heard of private schools before that age, so I had no preconceptions.
What gender are you? Mine was an all girls' school, and one of the cheapest in the country, so if you're going to a boys' public school I won't bother giving you advice.
However, if not;
I have plenty of experience with comprehensives too, because my Mum was a teacher. In my experience, the main differences are;
- Everyone is pushed more, and entrance is paid for and on academic merit, so there is no 'lower tier' of kids who just aren't interested. The flip side is people getting Bs genuinely believe they aren't intelligent.
- People at private schools can be naive about life and money. It's often not intentional. Personally I've never met any outright snobs, but I've heard that at other schools they can be endemic.
- There isn't a massive gap between lower end private schools and upper end state schools - the main difference is point 1.
- Life is just gentler. It's hard to describe, but I think private school students take longer to grow up, myself included. I was really immature when I started university.
On the whole, I say go for it - the academic support beats any other considerations by a mile.