I think you’re both right. The top private schools near us educate a lot of exceptional students, but also have plenty of above average or even average students whose families can afford to pay 50k/year to subsidize others. There are very few with entrance exams that are beyond all but the tippy top 8th graders. Frankly, it’s considered harder around here to get into the top public magnets than the really expensive private academies.
It’s really hard to say. There are public schools, even not-test-in, that serve very high-achieving families, where the kids are driven, enriched, often hooked, and mostly full-pay. The top 10-30% are likely all outstanding college applicants.
There are also boarding schools that allow them to reach well beyond their geography to accept students from a very high-achieving pool at rates that rival top colleges. Those schools tend not to rank, but a kid at the top of the bottom half will be very appealing to most colleges and even at the most selective ones, will probably be a strong student.
Likewise, there are public districts where the top student may struggle in college, not for lack of aptitude but owing to poor preparation, and many schools may be reluctant to accept a student and then crush them.
Mostly though, any student will be a different applicant as a result of what their experience has been. As you note, there’s a false equivalcy here. Students will be challenged and evaluated differently in any environment, and AOs are pretty good at understanding context. It’s one of the reasons they cover geographic regions.
I should have been more clear – i was thinking of rejective boarding schools, who, as @gardenstategal notes, draw from a national and international pool, and have admit rates below 15%. Those schools are not options for average students whose main attribute is they are full pay. The school I’m most familiar with has an endowment per student of $1 million.
I think it’s probably better to leave her at the current school and try to soften the competitive atmosphere from home. If you keep your college talks to fit and not prestige, your daughter will take the hint.
I think you don’t know what the public school will bring. Her new friends may continue to ultra competitive, or they might not care at all, she could be unhappy and her grades could suffer, the guidance counselor might be awful, etc. Of course it could all be great too but I’d probably stick with the known at this point than take a chance on the unknown.
I’d take it further. Kids like to talk about college - I’m going to Harvard but in the first year at least of HS, I’d let it roll off. WaaaaY too early.