I'd like to think I am in a good position to discuss this. I went to a state school for 11 years and then switched for Sixth Form to a private school and I can say that it was the best decision in the world.
My state school was a **** hole. To look at, it would seem a great school because it had good grades BUT it only pushed you if you were predicted A/A*, otherwise they couldn't give a toss. And if you didn't get it first time in the lesson, tough; you're obviously just retarded. I know people that resat some of their modules 5 times in order to get the best results possible. They refused to let you do the subject you were passionate about, instead making you do the subjects you are good at, hence why as a 'science student' I now study History! 9/10 of the teachers couldn't care, they were verbally abusive to students. In fairness, 2 of my top 3 favourite ever teachers came from there but it was either really good or really bad! They had no sports teams in place and you were discouraged from doing sports because it interfered with your academic achievements. Pastorally, it was even worse. I was bullied for 2 years, to the extent where people were sending me death threats and the school did nothing. Why? Because the problem was too widespread to deal with. In fact, they cancelled my meeting with an Ofsted inspector because I would say bad things about the school. Fantastic. Amazing. I know multiple people from there who have ended up either in therapy or in mental institutions. All in all, it was horrendous, and I have never, ever encountered such stuck-up, snobbish, bratty people in all of my life.
By comparison, my Sixth Form was incredible. It was roughly the same size, so no one can play that card, but everyone was a human being! The students were incredibly supportive of each other and 99.9% polite and respectful to each other. Obviously their were some issues, but they were dealt with quickly and actually dealt with, not pushed under the carpet. The teachers were literally my home from home. I've had a really rough year with medical problems, and the school were brilliant. They gave me so much support. We had 3 hours of sport a week, we organised House dinners, we went on trips. My head master couldn't give a toss about league tables and encouraged us to follow our passions; and before people say 'Well, didn't everyone just want to go to Oxford or live off the inheritance?', no.
I guess my view is slightly biased because of how **** my state school was, but everything that a private school gave me wasn't money related. It gave me the confidence to talk to my peers, taught me to speak to adults clearly, and also gave me enough self-confidence to hold my head high in the company of people that reduced me to almost nothing.