The people are not the same. The teachers are not the same. :L
That's why people tend to 'hate' private schools so much. Teachers push you more, and classes tend to be smaller so each individual student gets more attention. The people all tend to be rather wealthy, too. This means fewer students come from poorer backgrounds, and will presumably be less disruptive in class.
In other words, the learning environment in private school is, quite frankly, optimised.