I moved school to do my A-levels and I think it's not an understatement to say that it was the best thing I ever did!
I grew up in the Emirates, so the concept of state and private doesn't really come into it - all expatriates paid to send their kids to school. I moved from a vast international school (it's called Choueifat and IMO it is a terrible institution) to a much smaller girls-only school, right after finishing my O-levels (which they still did over there in 1998). I didn't know a soul in the new place, but the classes were much smaller and the teachers actually knew our names and cared if we did well or not. I made friends after a while (let's say 6 weeks) and did much much better in my A-levels than I could ever have done in my previous school, which allowed me to get into a much better University in the UK than I otherwise would have.
Also, at my previous school they had a ridiculously complex international curriculum and I struggled a lot with no help. At the new school, I really became confident in my ability to learn; it came as a big surprise to realise that I wasn't as stupid as I'd thought! And as others here have said, developing independent study habits was very useful for Uni and ensured it wasn't such a shock when I got there.
So in summary, I'm pro-move :)