[aardvarks]

What ivy league and other private research universities excel at academically is scholarly opportunities outside class assignments.

This is actually true at any school. At large state schools, there are professors doing real research. The difference with the ivy leagues is very few students actually seek these experiences out.

I completely agree (having been at a large state school) that there are many professors doing high quality research at state schools. I think the difference is (as you suggest) the funding and competition. Funding and even for-credit programs for undergraduate research were (I found) much more limited at state schools. You'd have 10 students, all with straight A's, applying for a single one-semester research assistantship that'd grant 1 course credit. At the same time I know of ivy school subject-specific fellowships of thousands of dollars for summer travel/study for which perhaps only 2 or 3 people would apply simply because there were so many other opportunities available. The net result is that if you're at an ivy, that kind of experience is much much easier to get.