I’ll preface by saying that my feedback is colored by perceptions of Cornell’s undergraduate reputation (having chosen between there and another Ivy). Also, lay prestige—which I feel is what you’re getting at—depends on superficial factors that I’d dissuade against factoring into one’s final decisions. That said, Cornell is held back on a “hard” institutional level by a low per-capita endowment (the smallest in the Ivy League, if I’m not mistaken; note that its absolute endowment is nearer to the middle of the pack) as well as a lower number of Nobel Laureate and comparably distinguished faculty relative to (repurposing a school from your original post) UChicago. “Soft” prestige factors are a trash fire, but just check out Facebook’s Elitist Memes page for a look into how peer schools perceive Cornell. From being “part state school” to close to a century younger than any other Ivy and located in a beautiful yet isolated area of Upstate New York, Cornell is more often the butt of (in my opinion) shortsighted and mean-spirited jokes than even non-Ivy Ivy+ schools. These factors, of course, shouldn’t determine where one resolves to attend school in and of themselves. However, since you asked, that’s where the difference between UChicago, Stanford, and similarly prestigious non-Ivy schools and Cornell lies, in my opinion.