It's not even that any person is better than another... Classes at elite public schools like Berkeley, UCLA, UMich, etc. are more demanding than at any but a few private colleges.
And it isn't really fair to paint with even this broad a brush. The fact is that large public universities generally have a broader charter than small, elite private schools. This is a factor of how they're governed on the one hand (things like mandating x% of students are admitted from in-state, or enforcing affirmative action), and the fact that they [usually] have to provide a reasonably comprehensive set of study options on the other. I went to an "elite" state school and studied history & comparative religion. My wife went to a small private women's college (~750 students) and studied biology. The resources available at my uni, which has a $2b/yr operating budget, were orders of magnitude better than hers, but the education I received was far less personal and -- again speaking in generalities -- not as good as what she received with the small class sizes and personal tutelage from her professors.