I have done teaching placements in a struggling state school, a fabulous state school and a fabulous private school. If I were to have children inthe area that I am now, these would be my three options. Knowing what I know about these three schools and if money wasn't an issue, I would choose to send my child to either the struggling state school or the fabulous state school.
The struggling state school had fantastic discipline and teachers that loved those children. 99% of the children there were from socially deprived families but I can honestly say that the teachers gave them the best start that they possibly could and I was proud to do a placement there. They may well be only 'satisfactory' in terms of Estyn (Welsh OFSTED) but they are extremely well thought of locally.
The fabulous state school is exactly that, fabulous.
The private school was undoubtedly full of good intentions and the teachers were lovely (as were the children and parents.) There were Harry Potter days where the parents were sitting in the school kitchen making decorations for weeks before hand, we had free rein to teach whatever we wanted and yet the heads couldn't afford dinner ladies so the teachers had to supervise lunch hour, which was spent in the class room with no hot option - lunch boxes only. There were no after school clubs (although this did not matter really because all the children, without fail, were lucky enough to have wealthy parents who could afford to enrol them in things outside of school) and the class sizes were tiny. Think 14 children in a class from reception to year 3. I am all for small class sizes and can talk all day about the benefits of bespoke learning, but I also enjoy advocate the social aspect of school.
I think what I am trying to say, in a very long winded manner, is that for me it would depend on the actual school. Private, to me, does not automatically equal 'better' just look at Queen Ethelburga. As well as that, for reasons that I can't quite articulate, I would not consider teaching in one.