Honestly, I don't think this can be said often enough - it depends entirely on the local choices you have available.
My dcs are at a private prep school and are thriving. Academically the school is good, but the thing I'm happiest with is the outstanding pastoral care. I would say the racial mix of the school is far better than we would get if they went to our local state option - I'm not sure I can say the same of social/economic diversity (there are certainly people who clearly struggle with the fees, but there is no-one I'm aware of who is really truly poor as I'd define it).
For me, I still think my heart is in the state system. I was state educated, but my education was pretty poor. Not just in academic terms, but the aspirations were just zero. I remember going to see the careers adviser and saying I was interested in doing a law degree - he literally laughed, looked at the name of my school, and said "no chance." As it happens (and with no thanks to my crummy secondary) I went on to get a law degree and worked for some years as a lawyer in the City. Great you may say, but it was bloody hard work doing it with so little support.
DH on the other hand went to an amazing grammar school and I would say had a better education than many who've been privately educated. My aim would actually be to move to state at 11, but I'm not sure how viable that will be.
Other than going on personal experience, I'm just not sure how useful this kind of debate is to your personal choices. We all have our prejudices, this is an emotive subject, and without knowing your dcs it's hard to even begin to advise.