Everything is very state dependent. If your child ever needs special support like speech or special education, it is going to be lots harder in a private school. Private schools can also hire people that do not have a teaching license. They are a lot less diverse typically because they can pick and choose who goes there. To me that is a massive negative. If you are wanting a religious schooling, then obviously private might be better suited. A disclaimer because I was a public school teacher so I’m very pro public education. As a parent it can be hard because maybe in some instances a private school could be better for one child. But private school is bad for society and kids as a whole.
I went to both public and private school before going to a boarding school and none of that shit is like television. Different set of problems. And a different culture. Private school kids usually have money and big issues that only get worse because they have money lol. They're not all created equally, so I can't really say private vs public. If the school has resources, adequate teachers, and a good curriculum, it's a go.