As a kid I went to a few different schools due to moving house and then went to the local school for high school (by then we were living in the country). My entire education was in the public sector.

I am now a teacher in a public school, so I can see things from that perspective too.

If it were me, I wouldn't recommend going to the same school all the way through. I agree with some of the above posters that changing schools at least once during schooling can be a good chance to 're invent' yourself. I see so many kids these days who can really benefit from a change after finishing primary school. This is especially true for those kids who seem to be given a hard time from others, they get a chance to start somewhere new and make new friendships.