My thoughts are more about the hidden curriculum though, expectations, manners, even things like establishing a good diet as they all have to eat together a cooked meal etc.
I also wonder about the length of day for children in a state school then having to come home and go back out to clubs, swimming etc whereas in independent schools this is all part of a normal school day.
I get where you're coming from, but I really don't think private schools have a monopoly on manners.
Far from it tbh. And I would say that the expectations at my dd's state school are exceptionally high, but that has more to do with the parents than the school IMO. Any school which attracts lots of parents with high aspirations for their kids will create a positive learning environment.
And my dd's state school is somewhat obsessed with healthy eating!
As for the day being long, I don't think it is really - dd does quite a few clubs in school, many of which are held at lunchtimes, and she does one after school activity at the school which happens straight after school. There are so many activities available that she could do something like that every afternoon, but I think it's good for her to mix with different circles of friends outside the school, so the other activities take place elsewhere. Usually, she comes home & has a bit of a rest, does some homework and then we go out again. It's fine tbh.
So in answer to your question, yes I do think you can get every bit as good an education from a good state school - perhaps with a bit of topping up here and there - as you could from a good private school. In fact, I'm another one who thinks that state can be an even better option.
Obviously, we are lucky to live in an area with outstanding state schools, and I genuinely don't think my dd could get a better education anywhere. We are in the fortunate position of being able to afford private education if we so choose, but I think it would be a complete waste of money at the moment. I realise that this isn't the same in every area, but I do think there is a rather misguided tendency to assume that private must be better just because you pay for it.