Some of the well-known private schools used to be for an aristocracy that barely exists anymore, and has been replaced by wealth, which is different. Therefore, the atmosphere may have changed, from what I have heard. At any rate before the 60’s, people, especially men, went to private elementary schools through 9th grade, then a prestigious boarding school, then an Ivy, then Wall Street or law or whatever.
I went to privates and did well, but the academic stress at a young age had a big impact. I sent my kids to a mediocre public all the way through so they could develop without that stress. The privates in our area have a lot of homework and kids barely have a chance to know themselves. Without a lot of homework, my kids read a lot and pursued “passions” outside of school which did, actually, get some of them into top schools, ironically.
That said, my youngest might have benefited from a small and personalized private, if we could have afforded it.
Think about your kids and what helps them grow in a healthy way. Obviously this also involves looking into the public and private schools available. Pay attention to “vibe” as well as substance.
Also, there is something to be said for being part of your community. I grew up feeling like an outsider in my town.