I did not receive better teaching at my highly academic selective private school than I have seen in my local state school. The teachers had 'good material', and they got good results. Some teachers were actually rather poor, boring and / or lazy - they got by because all the children were motivated to learn whetever happened. Sometimes teachers turn to private schools because they can't cope in the state sector. We had one who had been sacked from a state school for throwing a chair at a student (though I don't think she would be employed in today's more scrupulous market).
The best teacher we had - she was truly inspirational - wrote an article in a newspaper about a (teaching) relationship with a former pupil who is now famous and said how depressed she had felt durng her employment at the school because the views of the students were so predicatable, safe and complacent, and lacked the originality and unexpected delights of her former state school students. Looking back, I think she reflected our general outlook rather well.
I wasn't 'unlucky' with this school, it is a school I still see discussed in glowing terms on MN now. I also have no doubt that my DCs are taught by some teachers who are less than brilliant. But I feel confident that they are not being spoon-fed into the adult world as I think I was.
I think private school provide a haven from anxiety in todays uncertain times. Reading the press, and MN, it is easy to see state schools as a 'risk'. It is easy to see the mixed demography of state schools as a threat. It is easy to feel that you might not be doing the best by your kids, and feel the need to compete in some way that you can't even pin point for yourself.
If I had the money I might look at some private schools, but as it is I enjoy sending the DCs to the nearest, walkable school, and I see them and thier friends doing very well.