I only know a lot about high schools because I'm a hs administrator. K-5 schools the differences are generally smaller if you're comparing nicer schools. They are certainly better, but the research I've seen shows the outcomes are bigger when you look at high schools. Possibly because there are so many local religious private elementary schools? I'm not sure.

And fwiw I'm writing mostly about private boarding schools. I know a lot about them. Less about private day schools.

My wife grew up exceptionally poor and worked her way up to a top 20 law school down south for her JD and Yale for her PhD. She has 6 brothers and sisters and 4 of them are, or were, in prison. Only 1 graduated college. We met after she moved up here to CT. And she went to public school her entire life. Even public colleges until her PhD.

And because of that... I'm not a big believer in private schools in general. I want to support what made my wife and I who we are. I would never send my kids to private unless they were having issues in public schools. I think there is value in not being around a relatively homogeneous group of rich kids despite the fact that my wife and I could afford it.

I want my kids to have friends who are poor, who are something other than a token black person, or people who require special education etc. They are insular places that are far from being a slice of the real world. They're like utopias comapratively. It is possible that my personal bias effects my answer... but I tried to avoid it.

There are certainly advantages to private schools 7-12. The primary one being admissions to better colleges. Class sizes are smaller. Less school days. Nicer facilities. Less risk of violence. No or less standardized testing. SAT prep courses. They are AMAZING schools, and only a fool would ignore that.

My wife and I basically decided to balance two things... elite education vs exposure to the "real world" and opted for the latter. I don't want my kids to be elite--I want them to be well-rounded people. Some people pursue excellence and choose the elite education... nothing wrong with it. Now, our kids are doing well in school just like their mama. But no, they probably won't go to an ivy league school. We're white and don't donate any money--it wasn't gonna happen anyways.

Do you want elite education or do you want the real world? And if you choose the former, what are you going to do to ensure your kids don't end up out of touch? These are important things to consider.