Just a guess about the differences in engineering but probably comes down to professors and research money. The top schools attract the best professors because they get the most research dollars. Smart people also like to work with other smart people.
BTW congrats on Princeton. I hope it works out for you. I’ve known a few kids from our HS who’ve applied over the years. NMF type kids who didn’t get a whiff. Go if you can afford it.
It might have to do with the “toys” they can play with in their classes (including research). I know VT has a “highway to nowhere.” Not sure how many schools offer something like it. The more one can do (hands on), esp with undergrad vs limited to grad school, can make a big difference I would think. Book learning only gets one so far. The labs can do so much more. It’s one of the reasons Eckerd is such a top notch Marine Science school - they offer a ton, and no grad students competing for the experiences. With engineering, the toys can be very large and expensive. This tends to favor the large schools with funding.