*sigh*
Things that a public school HAS to provide that a private doesn't:
1) Transportation. How much money do you think it costs to fuel and operate a fleet of 25 busses a year? Not a single private school in my area had a bussing option. If you wanted to go to that school, you either drove there yourself, or you got dropped off.
2) Food assistance. The most that a child will pay for lunch at my public high school was $1.25. Almost half of my public school was on some sort of assistance that allowed them to get a school lunch for anywhere from $.75 to free. NO private schools in my area offered any thing remotely similar to a full lunch for this price. In fact, when I toured a private school (Peoria Notre Dame) it cost me nearly $3.00 to get an equally comperable meal. Food isn't free. Somebody has to pick up the tab.
3) Special education. Public schools are required to have special education teachers on hand. My public school of 220 students had 5 special education students on hand. Special Ed teachers are not cheap to employ. They have some of the most intense training out of any of the teaching fields, and have one of the hardest jobs in the school. @ 40,000 a pop for a teacher, you can watch your salary budget skyrocket. None of the private schools in my area offered special education teachers on hand. If you wanted privatized special education, you had to send your child to a "special education school".
4) Sports. Aside from booster clubs(which in my hometown had dick for support), public schools have to pay for all equipment, facilities, and uniforms. A LOT of private schools receive donations from weathly donors to support their athletics. One more thing that a private school doesn't have to pay for.
As for the college environment, look at that acceptance requirements for a private vs. public college.
I'd guess that on average, you see FAR lower acceptance qualifications at a public school than at a private school. If you only accept better achieving students, then I'd damn well hope you'd produce better scores than the public schools.