You should ask people to compare the schools, since many schools don't release match list data, especially not at the detail level you'd need to make such a decision.
In your case, I'd lean heavily UCSF, followed by Columbia. UCSF is only climbing the rankings, and is essentially in a run-off with Harvard and Hopkins for best overall medical school in the country. Choosing Mount Sinai over those if you're at all concerned with prestige, etc., would be a mistake. You don't say "I'm letting the bug get in my head" and then choose the #3 school in NYC alone.
If location is important, and you really want to go to NYC, you'd be better off with Columbia...again, if you care at all about prestige or rankings. You don't need to see the match list data to know which school has more prestige. If your concern is that you significantly prefer Mount Sinai (benefit of schools accepting people early, it builds loyalty

), will it hurt you in the long run? Depends. Some people at MS will be trying to match into NY-Presb-Columbia, while people at Columbia will be thinking of it as their backup match and looking to other places. That's the biggest difference I can think of, unless you're interested in something like radonc.
Finally: prestige does make a difference, if you care about prestige. As in, it will likely not make a huge difference in terms of your ability to match, but will make a difference if you try to match at competitive and prestigious programs. People at bottom 30 programs who get high board scores match into radonc every year - but even with a 270, they don't match at Harvard.
Edit: only using radonc because it's pretty much the most competitive thing out there right now. fill in the blank with whatever you want