As a parent that has had children in both, there is no comparison. It's silly to argue that there is. Sitting in a class with 10 kids instead of 30 where teachers can create their own curriculum and not teach to some test are two different experiences. The private schools are light years ahead of public schools in preparing the kids for college. I went to public school and took AP classes and still never had to do homework. College was a huge adjustment. Not that way for the private school kids. Most of them say college is easy compared to HS.
Better, just because you say it is? Maybe at schools ouside LA, NY, DC , but come on, this is Bawlmer, can't find those schools on any lists of top privates. I think your perpspecitve may be a little skewed living in charm city but skewed perspective seems to be a pattern with this bunch.
Many studies on this over the years - real data folks, not just anonymous blowhards spouting off - a little googling will get you there. Check out a popular book called The Public School Advantage that analyzes this in detail.