Barnard vs. Northwestern vs. JHU ED

“Make your best estimate, based on what you know about yourself- your strengths / weaknesses / preferences”

Sure, but one of her preferences is connections and job preparedness, in fact job opportunities is one of the biggest factors in choosing a college. Here are the top 5:

academic reputation
colleges graduates get good jobs
FA
cost
campus visit

"Trying to figure out the quantitatively “better” choice between those two schools is a fool’s errand: "

That’s what lot of people do, a fools errand would being judging a kid based on his or her priorities. The first four are all quantitative, it’s only the campus visit that gets into fit.

"best choice for you- which is the only thing that matters. "

The OP came here asking for advice between three colleges, two of which she hadn’t visited, throwing it back to the OP is not helpful, imo.

“but not the case for these two schools, for this student”

The OP asked which school was better for connections, so it is somehwhat important to her. My suggestion was that for pre-med, reputation was a wash, connections would favor Northwestern and campus fit would favor Bernard.