The thing is that not all state school are equal, and neither are private schools.
My DC both went to the local village state school for primary, because I wanted them to have local friends, it would have been a long commute to any private school (vs a 3 min walk), and I felt primary school was as much about socialisation as academics.
However, for secondary, there is really only one school in the area (live rurally), so we don't particularly have much choice. We looked at a few private schools that would work for us as a family logistically. In the end we chose a small private school where our DD couldn't just blend into the background, and as it happens, she's flourished, taking part in all manner of extra-curriculars, and excelling academically. She's quite quiet and unassuming, and I think would have just got lost in the large comp (or indeed a large private).
Our DS has autism (high functioning, so mainstream schooled). He basically started to go backwards in Y5 with an inexperienced teacher and poor senco support, so we moved him to private in Y6 (same school as DD). Again, he couldn't hide in the small classes, and although he's a very different child to DD, he too is doing a variety of extra-curricular clubs. He's now in senior school, and is finding it challenging, but I don't have faith that he would have had more support in the state system, certainly our experience was that the state schools just didn't have the resources available to them. It's not perfect in the private sector either, but we can meet with the school at the drop of a hat (vs taking weeks sometimes to meet the state school teachers/sencos), which is more comforting.
What's right or wrong for my children's education really is completely irrelevant for any other children, but I consider us to be fortunate enough to be able to afford a choice. I wish there was a level playing field in education, but currently there isn't, and we've just tried to do what we think is best for our children.