I wouldn't make this decision based on hospitals. Mount Sinai is pretty top notch... consider other factors like location within the city (if that's important to you; it is for a lot of NYers), curriculum, atmosphere, research/global opportunities (if you plan on doing either of these), student body etc. Actually, wait, go to Sinai if you want to speak Spanish, because that hospital serves Spanish Harlem in addition to the UES. In that regard, I would factor in hospitals (for patient populations).
Can't say much about NYU, but totally loved Sinai when I visited. I thought they createtd a really wonderful learning environment. Very supportive, filled with great people (students and faculty). But you know, that was just an impression on interview day. I really liked Sinai housing too. I've heared NYU really only offers dorms first year...