I don't know about public/private differences in general, but I think small private schools have definite advantages over large public schools. The small, private school my son goes to exudes a love of learning, but the kids there are allowed to move through the core curriculum at their own pace, so everyone is constantly challenged and engaged. Most classes have around 10 kids, so the teacher is able to individualize to a degree that probably isn't feasible in a large public school.
Our private school is also a relative bargain--again, I believe, because of its relatively small size. For one thing, there isn't a lot of overhead in buildings and maintenance. There's no gym, for example; instead, PE and extracurricular sports activities take place at a public park one block away.
In many ways, our small private school does "more with less."
