Are Private High Schools Better Academically Than Public High Schools?

There's a PDF summary at the link. The gist is that students at private high schools probably would have done equally well had they gone to a public high school.

Two exceptions are noted: Private High Schools appear to have an effect on SAT scores. Also Catholic Schools run by a Holy Order (such as Jesuit) actually did show some benefits.

Are Private High Schools Better Academically Than Public High Schools?
cep-dc.org

I went to a private grammer school, they couldn't afford a xerox machine but what I think what worked about the school is that they did more teaching and were very attuned to how each person is doing.