Trust me, the actual education is NO better than Tennessee at Sanford or Duke! Perhaps the prestige is better. Perhaps the social networking is better.
You get teaching assistants at big state schools. I'm not sure that's the case at Stanford or other prestigious colleges, and they have smaller classes as well.What's more, you stand a better chance of getting into a top graduate school if you've got an undergraduate degree from a top school. Certainly the networking would be better. That's not to say that you can't get a good education at state schools---you certainly can.