It depends on the neighborhood in which the school is located. Public schools in more affluent towns can and often are well funded, offer good facilities and teachers, and prepare you well for college. Even times of recession, your school won't be affected very much. Your school might even be better than the local private school.
Then again, if you go to an elite private school aka a feeder then you'll have the reputation and all of the benefits of a good public school and much more.
I went to prep school -- Andover -- and I loved it there. It's worth the experience I think. There's much more freedom to study what you want, but you do study hard. Also, the resources are phenomenal even without massive state aid.
However, you'll also find very bad public and private schools where drugs, violence, administrative indifference, and sexual abuse run rampant. No school is the same; it all varies (bylaws, amounts of state aid, reputation, donations, endowment, quality/commitment of teachers, condition of facilities, etc). The educational system here doesn't teach morals/ethics; you learn (or don't learn) that at home.
If you go to a mediocre public or private school, then, well, you're basically fucked, courtesy of the inadequate safeguards inherent in the American educational system.
As for Catholic schools, male students there have to watch out for potentionally shady priests...brave souls they are.
Ernest Hemingway once wrote, "The world is a fine place and worth fighting for." I agree with the second part. - Morgan Freeman, Se7en