Never. I was in both and will say with 100% confidence that there are VASTLY more life lessons learned when you're not in a bubble of the same socioeconomic people as yourself. I learned just as much on the bus rides to and from school as I did in my classes. Sure, a private school might have better facilities, but more often than not the attitude that comes out of private schools is atrocious. I know too many people that went to a private school or boarding school prior to college and came into it with the attitude that they were better than everyone else. As one guy in my fraternity put it "It all comes out in the wash". None of that sh!t matters in the end and there's a good chance you'll come off as some elitist douche rather than a humble yet capable individual.
What's this about a brownie in motion?