I work in Admin & Policy at a private university (not an Ivy), and we focus on these issues a lot at the office. Omniscient brought up a lot of very excellent points about the differences betweeen the Ivy League and competitive publics (did you ever consider a career in higher ed?).
There’s an idea about public universities that tends to be true, that is, you get out of it what you put into it. A good student, one who is motivated, participates in class, takes opportunities to meet and interact with professors and advisors outside the classroom, reads at least some of the suggested-but-not-required reading, takes advantage of study abroad programs or internships, etc. is going to get an excellent education at almost any public institution, and would most likely also do well at an Ivy. It’s not that the top of the standards is set so much higher at an Ivy, or other elite private, it’s that the bottom end is pushed up. A student who puts forward a “fair” effort might get a fair education at most publics, but that student would crash and burn in the Ivy League.
Size is also a factor. State universities are enormous institutions. Once they accept the best applicants, they must fill the remaining places with other students, so you might end up with some bozos in your class. Because the Ivy League schools are relatively small, and their reputations guarantee a huge applicant pool, they are never in the position where they must accept students to simply fill spaces. Actually, I should say seldom. For the first time, there is a growing sense that the Ivy League schools need to be more competitive in their recruiting in order to enroll the best students.
It’s hard to look at attrition to determine either the quality of student, or the quality of education at a school. There are about a million reasons why students drop out, and schools spend quite a bit of time and money to figure out what they are, and how to stop it. Did you ever hear of a freshman orientation, where students are told by the Dean to look at the student to their right, and to their left, and that one of those people will drop out? This might be a good scare tactic to use to motivate freshman, but in reality, schools work very hard to lower their attrition. It’s simply good business.
Ugh. This is far more than anyone wants to know about higher ed. On a final note, my office is currently working on a survey of the faculty, that among other things, asks them to rank the most challenging undergraduate programs in the US (excluding the tech schools, like MIT). The #1 response is not an Ivy, but the University of Chicago.