Per capita numbers between huge public unis and small LACs are tough to compare, though (even more so when the average quality of the student body is quite different) because huge state publics have many more majors/departments and huge publics tend to be more pre-professional (at the UCs, at least the faculty are an exception) while students at many LACs have more of an academic bent.
I had an NSF GRF in graduate school and have also served as a reviewer for the GRFP.
I would imagine that the relationship would still be pretty big. Since the NSF is an early career fellowship, a lot of it is predicated upon the strength of the work you did in undergrad and any interim time you spent between undergrad and the first year of your graduate program (mostly PhD).
I think an important takeaway from these tables is that you don’t have to go to a prestigious undergraduate school in order to get an NSF (or any of the other science fellowships - NDSEG and Hertz are the two other really big ones). You simply need to go somewhere that will allow you to get valuable experience in the lab with a professor who can mentor and shape you. Independent work is important - the more responsibility you assume in the lab, the more potential you display for eventually achieving independence as a scholar, which is one of the review criteria.
Also remember that the NSF defines “STEM” far more broadly than most people do. The “total” number also includes awards in the social and behavioral sciences: PhD candidates in psychology, sociology, anthropology, political science, economics, international relations, linguistics, geography, public policy, and history of science, as well as science and math education fields,
Liska21, thanks so much for doing this!!! It is so useful – I have been looking around for this kind of info! All I had was an outdated list of baccalaureate origins of STEM PhDs from a decade ago. I really appreciate this, and I am sure others will too!