I think the gist of the OP’s question requires broadening the schools in question beyond the monikered eight — include, say, Chicago, Stanford, Amherst, Swat, MIT, etc. Actual membership in the Ivy League doesn’t make a difference in education at top tier schools. It’s a question for another thread which schools makes it into that rarefied tier.
As an analogy, consider a general notion that is occasionally raised about the board; why some consider it a haven in the ‘net: the level of discourse and the overall quality of debate. Of course that needs to be taken with a grain of salt itself and there is a lot of nonanalogous imperfections, but the overall sentiment that what makes this board special and worthwhile is the (perceived) caliber of the population.
To help with the analogy, recognize that many posters here, if not already well regarded for their work or heavily involved with someone who is, will in time be disproportionately represented in other areas of the ‘net.
Now consider what it would be like if Cecil participated with regularity, and most mods were well known, highly regarded within their fields, and several of them were Nobel laureates. (Er, not that they’re not now!)
How fast would threads/classes move? How much below the surface of ostensibly simple questions could conversations and explorations go? I recognize that there are great posters and writings on other boards, but the signal to noise ratio is seldom what it is here. The overall elevated nature of the experience makes a difference to education.
Are some mods chuckleheads? Of course — not every professor is great. But the vast majority of them are towering intellects. Are some students content to get by with Bs and Cs? Of course, there are goons everywhere. At the top tier schools, however, there is a filtering process that doesn’t exist here, and the percentage of trolls and troglodyte is kept to a relative minimum.
So (to me) the most important difference between the tiers is in the overall quality of discourse on campus and how that propels the learning experience. Facts are facts, but the Core of a liberal arts education is analysis.