^^^ lot of info on Linkedin if you know what to look for. It’s easy for colleges to say Firm X is a prominent recruiter / employer on campus. Go to the Linkedin site for the school. See how many kids work for Firm X. In what role? Where? for how long? Compare that to how many kids go to the school. And how many are in a certain major.
Broadly stated, School X may have 100 alumni at Company Y but has 20k students. School A may have 50 alumni at Company Y but has 4k students, so school X has 5 times the students but only twice the placement. I would argue your chances are better at School A. Then you dig down deeper and find out the # of kids in a major is 10 times the number of A at X so the disparity is that much greater. An extreme example would be 20k students, 2000 in a major , 500 graduating, 100 placed from school x. 4k students, 200 in a major, 50 graduating, 50 placed. I’d much rather be in the smaller school. 100% of the graduating class placed at firm X (or similar firms). To me, that is a great example of the ecosystem the smaller, and perhaps more prestigious school has. It’s designed to send kids to top companies.
I realize that would be an extreme case but you can easily see the pattern by digging into the numbers on Linkedin.