If the state schools were good, I would have no problems with sending DC to state school. In fact, we are probably going down that route for infant school, but are likely to switch to private afterwards.
I went to state school in another country (grammar during secondary years), my brother went to private school first during his primary school years, and then switched to state (grammar). Weirdly enough, he went to the private school because I - as a teenager - convinced my parents to do so. I used to help out at the private school, and couldn't help but notice how much better behaved the children were.
If I wanted to offer my DC the same experience I had at state school all those years ago, my only option would be to go private. We lived in an affluent area, and at the time the local state school had maximum class sizes were 20. At my school, they were around 15-17. Class sizes are around 30 where we live now. The same goes if DC qualified for grammar school.
I would want a selective school for DC as I attended a grammar - and seriously would not have coped in a comp. From my experience, those kids who weren't as able would label knowledge as 'uncool', and hence, could impact your motivation. I'm afraid that does happen a lot even now. Maybe I lack the political correctness of some Brits, because where I'm from splitting out secondary school by ability is the norm. But who knows?
Long story short - if state school could offer small class sizes (max. 20), and also had grammar schools throughout the country with equally small class sizes, it would be a no-brainer, and I would choose state rather than pay for private. But I guess there's a greater chance of a pink hippopotamus falling down from the sky than that happening.