small groups of kids brought up similarly learn better than large groups of kids from many different backgrounds.
You forgot - taught by those who love them most and know them best...
That too. Although I think it probably is a bonus compared to what I posted. I would guess private schools (especially parochial schools) are much closer to home schooled students than public.
I don’t know if my mom or dad would have been equipped to overcome my learning disability in a home schooled environment. They did pay for and make time to drive me to the learning center to overcome it though. And that one-on-one time with a teacher probably had as much to do with my later academic success as anything.