It depends what you are interested in.
My kids are at a state school - Y10 doing really well, predicted 8s and 9s. Has nice friends, has a social life, has a part time job. Finds school busy and tiring but is coping well with it. Y7 is an outgoing type, has met lots of new friends and a girlfriend (!). Both good at taking responsibility for their work and both keen to achieve. They get really good study skills guidance and help with planning their work and I really don't get involved as they are very bought into it.
They went to the nursery dept of the local private boarding school (free 15 hours!) so we know a bit about it. It doesn't get such good results as our state school but facilities for everything are much better, the place is calmer, fewer kids and smaller class sizes.
In our school there is no way enough space for all 1400 kids to sit down and eat lunch. My take packed lunches and so far as I can work out they eat on a bench outside or wandering about. which I don't like much.
At the private school there is a proper dining room, sit down lunch with the staff and home cooked food. They used to go for lunch there in nursery and even at that age were being taught manners, offering to pass things etc. I really wish there was some of that at the state school.
Sports facilities are way better at the private school - neither of mine are particularly sporty so it doesn't matter too much, they just do it for fun/fitness, my youngest does sports out of school instead.
I think there is a greater range of children at the state school. Lots of bright ambitious ones but also plenty of kids with behaviour challenges, we do from time to time hear of X who set off the fire alarm again or Y who got in to a fight with Z.
I do think your private school fees perhaps buy a calmer experience with less children with additional behaviour needs, good facilities and a training in how to behave socially eg at a drinks party, hand around the drinks, if you meet someone, shake hands and look them in the eye.
Some private schools can be extremely pushy and competitive, though of course, not relaxed at all.