I think it is about the right school for the right child always.
Both have pluses and minuses, aside from the actual cost of private.
These debates always turn unpleasant though, with snobbery and superiority on one side and resentment and jealousy on the other.
I am really pleased my older son went to a comprehensive though I, like you OP, assumed private was better, but my ex wife had no interest, and he wasn’t cognitively ready to sit entrance exams to the best privates in any event.
He achieved a fantastic set of GCSE grades (maybe he would have got a few more 9s and a few less 8s at a private, but he did it substantially independently, developing a fantastic work ethic in the process and I am convinced will get better A levels because of it), he got into a very competitive grammar which I only learnt he was applying for at one of his parents’ evenings, and he gets on with everyone from what he calls ‘road men’ to scholars at one of the very upmarket local private schools.
My younger son is also doing great at the same comprehensive but his needs are different and, though I am convinced that he will do fine at GCSE s, he has some needs which I feel might be better met doing his A levels at a private school, but we shall see.
The one thing these threads do all have in common though are parents interested in their children’s education, which is a massive win in itself. You would be amazed how many parents just aren’t that invested (at private too; they feel that they have done their bit when the bank transfer goes through).