When I was accepted at NYMC, I was also offered a 15,000 'scholarship'. However, half of that sum was truly free money and the other half was a low interest loan. If you are trying to compare costs, I would be very careful in making sure that the money is really free.
I would choose Downstate over NYMC. Simply due to the fact that you can choose to live in some very culturally diverse (and awesome) areas in Brooklyn. You'd be very close to Manhattan too. I would prefer to live in an area where I am a subway stop away (or a few) from lots of exciting things to do.
There most likely is very little difference between the schools in terms of educational experience during the first two years. However, NYMC may be a little more intense during the first year. I've heard (this may just be a rumor) that NYMC bombards students with exams during the first year. That just doesn't seem to pleasant to me.
I'm not familiar with the clinical sites that NYMC students rotate at. I only know that they can choose to rotate through St. Vincents. You would receive an excellent education through Kings County via Downstate.
Honestly, the biggest difference between these schools will be your surroundings. The choice boils down to where do you want to live- NYC vs suburban Westchester.