Match lists at Vandy are more interregional than Emory. This could easily reflect a bias in the student body, but there it is. As topsurgeon implies, Emory is falling in the rankings (now 21 - no longer in that "top 20" tier), while Vanderbilt appears to be improving. Emory does quality basic science research, but Vanderbilt has a better reputation for research both nationally and internationally, while Emory is more regionally focused. My personal experience: a number of my west-coast friends (not involved in the med school application process) had never heard of Emory, but knew well Vanderbilt's reputation.
They are not the same. Their focuses (just look at Grady, the CDC, and Emory's global health program) are not the same. While Vanderbilt may do better in a research ranking, it doesn't make it a better overall school.
A neurosurgeon isn't going to be struggling to make payments even if that debt grows to 300k, nevermind they could do an academic program for 3 years following their significantly longer residencies and have most of it forgiven. Suspected specialty can play a role if you know what type of person you are - but, as Tots mentioned, you should be aware that you may decide you want to do family medicine someday, and thus consider that when looking at financial aid packages. Overall, though, it's easy, obvious, natural, etc., to wish you didn't have the debt while in residency, but, speaking in the long term, I wouldn't make it a dictating factor over other personal interests (unless you're die-hard primary care. Accruing 300k in debt to go to a noncompetitive residency wouldn't be your best move).
Other people may have different experiences, but those are the ideas that educate me. This is mostly irrelevant, and assumes the decider has no bias one way or the other. If you feel a stronger affinity for Emory than Vanderbilt (I know a number of people who feel this way) then you should choose Emory.
TL;DR: Feeling comfortable and happy with your choice is worth far more than status - that's why every year a number people turn down Harvard for other schools.