"what's so great about private school?"
That's quite a broad question, really. For some private schools the answer may well be "not a lot"- or rather, they aren't any better than state provision and may even be worse than some of the better ones. For some children, a particular private school may not be better than a state one. I think it all depends on the individual child and the school. In my view, it not all about academic achievement or whether the child goes on to be a judge or neurosurgeon or business leader and so on. These things are important, of course, but education and school should not just be about exams- I want my DC to be happy and settled at school too. I want them to be able to find sports/activities/hobbies they are good at and love to do. If you can find a school that allows your child to do all of those things, then great. It matters not one jot whether that school is private or state because its the right school for your child.
However, there is no doubt in my mind that there are some excellent private schools who do offer wider opportunities than the state can. Which is entirely understandable given the funding, resources and facilities they have available. That is not to say that a good state education cannot take you every bit as far as a good private one. But it can make school days very different and open opportunities that may not have otherwise come your way.
My DC are at private prep. It's a lovely school with strong ethos and academic rigour, small classes (more than one form in each year to allow this), lots of sporting and extra-curricular activities. I feel it has been a good fit for our DC. It may not be for other children though- I have a friend who moved her DC to a different school as she thought it was too academically demanding for her DC and they are happier in their new school.
Our local state provision is pretty abysmal, in particular the local senior schools. For example, one even got to the point of asking parents with any maths skills to come in and help as they could not recruit sufficient number of maths teachers. There is also talk of closing schools on a Friday, or having a half day, in an adjoining area and this has been discussed for this area too. A friend moved her DC from one of these schools as he was being allowed to drift academically- he's clever and as so many classes (esp science and maths) were being taught by non-specialists on a regular basis, once he'd done the basic work set out they didn't really know what to do with him. He was unhappy and felt that a lot of the time classes were noisy and disrupted, and teachers spent lots of time dealing with that. He is much happier where he has moved to (private, academically selective), but I think that environment would not have been conducive to a good education for a child of any ability. How can you learn in a classroom full of disruption? As a teacher, if you don't know the subject then how can you stretch a clever child or support one who's struggling with a particular concept, or indeed help a child who just isn't particularly academic?
Taken together, I don't think that's good enough and so we have chosen an alternative. I am well aware that we are very fortunate to be able to make that choice. It would be great if all children could have a good education, but the reality is not all schools can provide that. And that isn't all down to the school itself. I think the teachers mostly do an amazing job but are hamstrung by the education system itself, by poor behaviour and lack of effective discipline, but also by lack of resources to support pupils appropriately (whether that is pupils with SEN, pupils who need stretched academically, or those with problems at home and so on). I can't singlehandedly change that by choosing to send my DC to a failing school. It won't make any difference to the school or to the success of other children in that school. It will make a difference to my the education my children receive though.
I went to a bog-standard state school. It wasn't the worst in the area, it was considered slightly above average, but not the best. I achieved quite well academically, but that was not really down to the school. If you were well behaved and got on with your work, and achieving reasonable results then not much attention was paid to you by the teachers, bar one or two outstanding teachers who did push us to keep doing better. Being academic wasn't "cool" though and although I wouldn't say I was bullied, there was a lot of teasing/name calling and unpleasantness. Luckily, it didn't really upset me and I had a good group of friends anyway. Most of the worst offenders left at 16 anyway, so less noticeable after that.
My DC