This thread will go backwards and forwards ad infinitum as there are so many schools in both sectors.
But, I would say, very generally, that private schools do have a lot more support (look at the staff:pupil ratios), more enrichment available and an easier (not necessarily better) learning environment. If pupils struggle in busy chaotic environments then the private option is probably better.
It is also true that private schools, on average, have teachers with stronger subject knowledge, as they pay up for them (I was one!). But that doesn’t mean better teaching necessarily, but it is maybe a plus for the very strong, especially at A levels.
The upside of state is the shorter days for parents who want to do what is slightly condescendingly called state + (which I suspect some private school parents think is the equivalent of flying premium economy). Another way of looking at that is called parents who who want to, in old fashioned terms, parent. That is help with homework, facilitate out of school hobbies etc. Both my children have a main interest out of school at a higher level than would be available even in the top public schools, and they can do it earlier in the day and still get prep done.
In addition, I do think that if you can manage in the slightly more chaotic and less supportive atmosphere of a state school, it does build genuine resilience, which is not the same as two days of walking in DofE or Trips week.The biggest lie private schools tell is that their pupils are resilient. Of course there are some, some people are naturally resilient and parenting plays a big part too. But, if you are overly supported and not allowed to fail and learn, you won’t build resilience.