what you'll find with the average universities is that they usually have a specialty program that brings in elite students and the rest of the university is average. The elite universities will be very selective in general and have a better average student body and multiple elite colleges - law, business and economics especially.
The very elite universities will have higher thresholds to get in and more resources. But, it's the students that make the university elite, not the university itself. I've found that a lot of profs from the school I went to (which was ranked top 10 overall in the world when I was there) had actually rotated to and fro to other lesser universities. The instruction was the same, but the standards and competition weren't. What you need to produce at the elite school will be greater to get an 'A' than at the lesser school. An elite school is simply concentrated competition. You can get a great education at a 'lesser' university, you just won't be as pushed and you won't be as marketable once you leave.
It is about branding. People attend Harvard or Yale not because a particular professor teaches there, but that it can be very valuable for marketing yourself post graduation.