(or, more pessimistically, larger universities tend to have disadvantages that individual profs and departments might or might not overcome...)
There certainly are significant differences between individuals, but nearly everyone is smart and scientifically motivated.
(Many students left before graduating, maybe half, but it was only rarely because they couldn't do the work. My good friend had to leave for medical reasons, it was very sad. Another left as a sophomore. 10 years later, he asked if he could come back, and the Institute said "sure", and he graduated with straight A's. I asked him if he'd gotten smarter in the preceding decade, he laughed and said no, it just took him 10 years to get ready to work hard.)
On the other hand, most Stanford guys I've met have also been sharp, and they graduate 700 PhDs a year according to someone below.