There is no ideal school. That's why discussions about this subject matter draws such heated varied responses.
What I would want from the state system may not be what others want. It isn't just a choice between private v state. It is about 'what school is right for my child'.
You might find comps where the top set is stretched, but where the bottom will lack aspiration. You can also find the opposite, where the top is left to deal with things on their own, while teachers concentrate on getting the lower set to get them to pass, so that league table numbers look better. I'm yet to be convinced that a school that caters to the whole spectrum actually exists.
You will see loads of private school threads where people will say that e.g. Winchester may not be right for their son, but Rugby is. Now, those are two schools in the private sector... and even then, one may be a better fit than the other. From what I gather, at a state school, you often lose the freedom of choice.
For those who have money to spend, I believe that a great part of what they are buying is exactly that - choice. Yes, these schools will be selective, but it's not like in the state school system where you are at the mercy of postcode lottery. So you can go and look for a school that is right for your child.
As mentioned before, one of the schools I attended for a brief moment in time (and which is the one I liked most) was a US high school - which is basically a comp. However, postcode lottery meant that the school (which was in a very wealthy area) was much better equipped than many private schools over here and the intake were very well-behaved children of doctors and lawyers. Hollywood frequently uses that school in films/TV shows set in a US high school - and we all know that Hollywood does not often portray what is the 'norm'.