I don't think that either school system has a monopoly on decent people and obviously there are awful private schools and awful public schools just as there are great schools in in both systems.

On the subject of diversity I can speak only from my own experiences. I went to private and public schools and whilst there was certainly diversity of cultures at my private schools at the public schools there was far more diversity amongst students, staff and parents. It wasn't just a matter of cultural diversity but also there was a far greater diversity of world views, sexuality, political views and economic diversity as well. At the public school I attended there were gay teachers and parents and as a result of this openly gay students as well. At my private schools I have no doubt that some students were gay but I have no idea which - they weren't out. Of course there was some diversity of world views at my private schools but to my knowledge none of the parents or teachers were leading such activley alternative lifestyles as some of the community involved in my public school - none of the private school teachers were goths and none of the parents lived in communes lol.

As far as the very rare families that don't care go, thier children leave school in year 10 unless they genuinley want to be there and there was just as many parents who were uninvolved in thier children's education at my private school. I noticed very little differance in the numbers of disruptive students in either system (I think I was one of them rofl) and TBH the teachers in the public school seemed more committed to our well-being than the teachers in the private system. A few of my public school teachers had successful careers in thier fields but chose to teach, none of my private school teachers had practical experience in the areas they taught.

My private schools did offer more extra-curricular activities but TBH if my children want to join a choir I can arrange that without the assistance of a school.

For a while we considered a private school for primary because of the extra possibilities of language instruction but I'm more a fan of immersion so I think my children will learn more from 3 weeks in a country than a year in a classroom

ETA - In terms of economic diversity even parents who are struggling to send thier children to a private school can be assumed to be somewhere near or above the average income - it's not likely that they will be far below it.
TBH I felt sorry for some the children who's parents were struggling to afford the school fees. It seemed like they felt the responsibility and they were carrying a bit of a burden, of course others didn't feel it and had no problem lightening up occasionally. One of the girls had never been on a holiday with her family!! That freaked me out.