Mixture.
Community nursery school - brilliant.
Community primary school - did very well by both of them. It was roughly in the middle of the SATS league table for our Inner London borough and class sizes were 25-30, but there was plenty of support for children struggling and for children who were whizzing through the syllabus. It had an intake that matched the very diverse area pretty closely, in terms of social background, ethnicity and spread of abilities.
Unfortunately when it comes to secondary school, not many of our local comprehensives get an intake like that. So:
At 11 daughter went to girls' comprehensive school. Good school, pastoral care pretty good (much needed), academic results way above average for an inner London comp (and above national average) but not a perfect school by any means. For sixth form she transferred to an independent school, purely because it was the only place she could do the A level subject combination she wanted. It was a very different environment. She would never have got in at 11 (not good enough at tests, particularly maths) and she got some of the lowest A level results in her year but I think it was a very good move in most respects. Daughter loved the fact that everybody there was clever and that working hard was the default option.
At 11 son went to independent boys' school with a scholarship (discount on fees, we still have to find the majority). He's in the sixth form now. It has been absolutely fantastic. We went for that rather than one of our local comprehensives because if he'd gone to one of the ones that could offer him a place he would have been in a tiny minority of boys of his level of ability (to put it bluntly).
At a lot of our local schools there was (it's changing now, I believe) not much going in the way of extra-curricular activity (no interest from pupils) and being bright, well-behaved and hard-working was akin to turning up at school with a tattoo on the forehead saying 'Bully me'. The ones that take more than a handful of bright children per year group are hugely oversubscribed and we didn't get a place at any we applied for.
At the school he goes to, there is a very academic curriculum, vast range of extra-curricular stuff to get involved in (and peer pressure to do so) and because it's a big school the intake is more diverse socially and ethnically than some of the outer London grammar schools we could have sent him to if we'd been prepared to turn him into a long-distance commuter at 11.
You can't generalise across the UK about why people go for private rather than state. It varies so much from place to place, child to child, family to family, school to school. We wouldn't have paid if we could have got what we considered the essential minimum from the state for either child. But we couldn't.