I actually just made this very decision! I ended up choosing Downstate, but I believe that both schools are wonderful schools and that you can't really make a wrong choice if those are your options.
Downstate has a smaller class size. NYU's class size isn't what I would consider big (it's around 50 students) but Downstate's class is really small at 30 students. I like small class sizes and feel that in a 30 person class I will always be getting personal attention.
I feel that Downstate balances its schedule a bit better than NYU. Look at their schedules and curriculums online to see which balance you prefer for yourself. In addition to an overall balance of when you are taking classes, it bothers me a little that anatomy is split up into two sections at NYU (you do lecture in the fall and lab in the spring).
I attended classes at both schools last week (something that I would recommend you do to get the feel of the program) and enjoyed the classes at both. I found the class I went to at NYU to be slightly more interesting, but I didn't see a huge difference in the quality of the teaching (and think the difference in interest might have just been because of the topics being taught the day I went)
The pass rates for the NBCOT for the two schools are both high. I think they are within 6% of each other, which means that it isn't really a big difference.
In the New York City area, the two schools are equally respected. I can't speak for other areas, but I know that in the New York area, at least, there is little to no difference in ability to get a job graduating from Downstate or NYU.
I've spoken to students from both of these schools and they seem equally happy about their education and career prospects. However, one or two students at NYU told me that they would have gone to Downstate if they got in.
Neighborhood-wise, there is no denying that NYU is in a much better neighborhood. It is a cool and fun environment to be in. Downstate's neighborhood is nowhere near as cool or nice. However, it is not as ridiculously dangerous and bad as some would have you believe. I wouldn't hang out there (there is really nothing going on, it's located in a pretty residential area) and I probably wouldn't feel safe walking alone at night, but those are things that you really don't need to do.
Good luck on your decision! And maybe we will be classmates next year.