I've always wondered. Do you think someone studying Medicine or Mech. Eng. at Harvard wouldn't get a higher quality education than what many public colleges provide ?
One of my professors at an ivy would occasionally at the end of a lecture jokingly say something like, "ok here's what I think about all this, this five minutes is what you're paying 30 grand a year for so pay attention, everything else I've said today you could have read in the textbook. Nobody actually uses this algorithm, if you need it you're already overloaded, people just buy more capacity before utilization gets this high."
At the undergrad level I think the main benefit of a high end school is simply being grouped with other high end students and so getting a curriculum tailored for you. As if the Honors and AP classes in high school were only available in a few schools that were selective and more expensive.
I don't think this is completely true but I think there is a lot of truth to it... you go to fancy schools for the other fancy students as much as anything else.
Point being, at the undergrad level Harvard isn't better because it's Haaaard-vard, it's better because their curriculum is more advanced, which they can do because they have sufficient concentration of high-talent students who can handle it.
I can't speak to the quality of STEM education at top-tier universities, but having experienced humanities at a mid-level state school and watched a fair number of lectures for similar courses from Ivies, the main differences seemed to be:
1) The professor might be someone you've heard of,
2) Guest speakers/lecturers are both A Thing and are usually very important people (highly placed in government, NGOs, or corporations),
3) The students are way more engaged, which I think is a result both of actual higher levels of student interest in the material and more of the students having come through a K-12 education that was participation and discussion heavy (see: how most major prep high schools run their classes) so being used to behaving that way, because that's just what one does.
IIRC the consensus is that a Harvard undergrad education is high-quality, but not exceptional. The experience (including the networking, and the access to people and opportunities it grants) is what drives people to its gates.
If you want an exceptional education, with access to the hardest courses available, you go to MIT.
Yes, MIT is a level above. I have an M.S. from a good state school and took a graduate course where the text was SICP (Structure and Interpretation of Computer Programming). At MIT that's the freshman course text book!