I went to a Jesuit high school. I learned everything I should have but what made it different is they taught us not to be fucking assholes.
Teachers there didn't coddle us. We wore ties every day, and I remember the vice principal (who was scary as fuck, was in Vietnam, pretty sure he had a Brock Samson-style knife strapped to his leg) walking down the hall and grabbing my loosened tie then giving me what they called Penance Hall. We didn't have detention, they put us to work taking care of the school.
We also were taught to think for ourselves. If we were sure of an answer, we had to be able to defend it and explain our thought process. There was very little regurgitation except in fields that required it (ie math).
We talked about religion; theology was a class. But it wasn't "God is good, love, jesus mary!", it was more about critical thinking, and framing religion in the sense of helping your fellow man. Seniors were required to go do community service every Wednesday, usually at poor public schools or helping children with special needs, in addition to our normal community service requirements. We had mass every Friday that was mandatory, but really it was a chance for the Jesuits who worked at the school to talk to us. The school's motto was "Men for Others".
You can't do that in a public school. I think that is the real difference between (most) private and public schools. Talking with friends that went the public school route, more of them hated their schools and basically were taught to memorize and spit out what they had read.
I graduated in '07 for what it's worth. Wasn't that long ago.