@kencc83 i dont think the distinction OP is trying to make refers to the USNews ranking position by position. i dont think most applicants take USNews that literally anyway. They are rather asking whether the elevated status of HYPSM in terms of desirability/prestige compared to the other top 15 schools is grounded in substantial differences in opportunities offered by HYPSM vs the other top schools.
@roethlisburger definitely true. There is definitely a feeling you are at a richer, more gilded environment without practical budget constraints. You get small everyday perks that you do not get in other top schools. That is especially true at Yale and Princeton due to their huge endowments and relative focus on undergrads and their smaller sizes. One of my best friends was at Yale while I was at Penn, and whenever I visited the difference between Yale and Penn in terms of how rich the place felt was definitely noticeable. Also the Stanford campus is a complete utopia that oozes big money.