There are a lot of assumptions on this thread, and some unnecessary vitriol.
I can't answer the OP's question as it was a route that we didn't go down in the end, although we did consider it carefully. In the end we went down the state school route, only sending DD to a maths tutor for GCSE for a couple of months when she needed it. DD achieved excellent GCSE and A level results at her (rather good) state school, and is now at a very good university studying a STEM degree. I feel that the only thing she may have missed out on is gaining the self-assertiveness and confidence she might have gained from being educated privately. In terms of academic success, none of her peers at private school have done as well as she has.
There are no private schools in our LEA, and those who go down the private route send their DC to private school in the next city, about 15 miles away.
The mixed sex school isn’t as academic as the boys or girls schools (which are part of the same foundation). As a result there are a higher proportion of less affluent pupils at the more academically rigorous schools than at the mixed sex school. The mixed sex school has had more problems with eating disorders, drugs and competition over positional goods. It is a very good school by all accounts with excellent pastoral care, but the parents there are generally more affluent, so the money for drugs and designer clothes and accessories is more widely accessible.
This is the impression I have got from talking to parents who have DC at all of the schools. Interestingly, we have one of the best state 6th form colleges in the country in the next county, and most of the students go there rather than do A levels at the private schools. They get a better education for free there.
Some of the issues raised about state schools, such as not excluding disruptive pupils are because ofsted is cracking down on schools who exclude pupils:
www.tes.com/news/exclude-and-youre-not-outstanding-ofsted-told-heads
If a school’s exclusions have risen sharply it could trigger an ofsted inspection.