This is an interesting discussion. I agree with several of the above views that if finances are a factor, especially if you have a well-rated public school just down the road, it is a no brainer. Your D seems like a bright student, so even if she is in a large public school, I was told that they place the bright kids in a special program of sorts so they still have the benefit of good company (like a private school typically offers) and good rigor and depth (that a public school with lots of resources offers).
For those who are fortunate to afford private school or boarding schools, then I think it is a matter of fit. There are some generalizable (but not absolute) differences: public schools are typically larger, more diverse socioeconomically, allow unlimited AP courses each year, but are also more competitive in athletics, have a more heterogeneous teach skill set and class difficulty, less guidance counselor 1:1 assistance; whereas private schools are smaller, more personal, less diverse (which can be good or bad), smaller class sizes, have a more holistic curriculum and may care more about “other factors” that make their students well-rounded, confident, creative, and liberal-arts educated, they allow fewer APs to be taken per year, but have generally harder classes, lower GPAs (e.g. hardly anyone in my D’s class have a WEIGHTED GPA of 4 or greater), lesser heterogeneity in teacher skills (i.e. more of the teachers are generally good to great, but nothing is absolute of course), more “sheltered” environment, perhaps more “rich kid programs”–language immersion and trips to various countries; esoteric summer camps, ski trips, etc.
Fortunately for us, we could afford a private school, so our D (also straight As like your D in all her middle school) genuinely looked at our public school (also one of the best in the area, not sure about “the country”) and her current private school (which she loved). Ultimately, she chose to stay in her private school. I think she chose well and chose the system/school that fit her personality. She is very smart, but did not have a lot of confidence; she places a lot of importance to interpersonal relationships which she got a lot from her teachers and classmates; while not a slacker by any means, she is generally not competitive, so she would have drowned in the zoo environment of our public schools; I personally am the complete opposite of her–I am/was (when I was in high school) pretty competitive, confident, willing to take anything and all the risks, easy to make friends with any gender/race/religion/background and would have chosen a large public school, or perhaps a competitive/cut throat private school. But I am not my daughter and she chose the school that fits her perfectly. Just like we advice kids to visit the schools before they select their college, I think the same thing should apply when selecting their high school.