Just like not all state schools are equal, neither are all private schools. Though people seem to think ‘state’ or ‘private’ are accurate definitions on their own.
State schools - local shit comp (I went to it), grammar, single sex state school (they exist), state schools Labour politicians send their kids to (London oratory, Grey Coat School London).
Private - the ‘public schools’ Eton, Winchester, Rugby, then the average private school and then the small local ones.
To suggest children can be described by the type of school they went to is pretty limited. We can all generalise Eton / public school toff old boys, vomit. But apart from that I’m doubtful.
I went to a crap state mixed comprehensive. We were lucky if we had the same teacher for longer than a few terms, kids had many issues all the time, set school on fire, huge class sizes etc etc. But I had fantastic parental support which made all the difference. I was confident, accomplished and happy - despite the shit school. I didn’t even know it was, at the time.
So my children understand social realities and understand how I’m sending them to private school. Because I can. Facilities are better, class sizes smaller. Do more sport (and more drama etc).
The politicians fcked the curriculum years ago. Not enough sport / drama especially - these things aren’t expensive (music can be). They really do give confidence to children.
If a child has parents who do not support him / her, it doesn’t really matter what school they go to.