The math major of a couple years back - graduating class in Yale was a little more than 10. The same year in Princeton was a little more than 30.
After few years, almost all of them in that class from Yale are in math or math related(applied) Ph.D. Programs(in Top 10 NRC ranking - and other one too in their specific chosen area) with fellowship for some. Some of them mentioned that they saw the same faces from HPSM during the Ph.D. (Accepted student) invitation events of multiple top 5 programs.
As one of the current students has said, there would be no difference among HYPSM for their undergraduate math programs. All schools including Yale gives you top level preparation for your adventure.