Just a few nitpicky corrections to otherwise very informative posts…
Looking at undergraduate enrollment is highly misleading. JHU has an enormous number of med applicants, far more than its size would suggest. Hopkins had 390 med school applicants last year, approximately half as many as Berkeley with 769, UT Austin with 733, and UF with 760 – although Berkeley, UF, and UT Austin are 5, 6 1/2, and 7 times larger, respectively. Some large public universities such as UMD College Park, Rutgers, Penn State, and UNC Chapel Hill actually produce fewer med school applicants than Hopkins.
Only Cornell has more med school applicants among private universities. Duke and Emory have approximately the same number as Hopkins.
Princeton is at least as strong as Hopkins in the sciences, so color me skeptical. (Program reputations rest primarily on research output.) Hopkins may offer specialized biomedical opportunities that appeal to some students, but I doubt most science majors at Princeton are suffering from a lack of research options. Note that all Princeton undergraduates are required to complete a senior thesis (i.e. a rigorous research project) for graduation, something few other colleges require.
The neuroscience program at Princeton is still up and coming. The new neuroscience institute building at Princeton has existed for only a year and a half.