Yes and no. One of the main facts to consider is that NYCOM's OPTI doesnt have an ortho residency, but TCOMs does. However, NYCOM students can rotate through Peninsula hospital, about 20 minutes from NYCOM, which does have a D.O. ortho slot, but it's under LECOM I believe and I honestly havent heard rave reviews about it, but then again, ortho it ortho. You go where you can get it.
The flip side....the greater number of hospitals will enable you to gain more exposure though. You can see a fair amount of volume when it comes to orthopedics if you can schedule your rotations to be at some of the coveted programs like North Shore Univ Hospital (ranked best overall hospital system in the country last year), also LIJ and Nassau University Medical Center have respectable surgery programs and do lots of ortho from what I hear. However, keep in mind these are very competitive for anyone to climb into, DO or MD. LIJ is associated with Einstein. Nassau Univ with Stonybrook. Likewise, you may be able to gain similar exposure at TCOM for less money. I dont know their programs well enough to give an accurate idea.
IMO, dont base you school choice on what place has the better residency associated with it, as you can apply to TCOM's programs from NYCOM and vice versa. Granted, they may be partial to their own students, but wherever you go, if you want ortho, you'll have to do well in class, shine on rotations, and rock the boards. The choice of school will not be the deciding factor in obtaining a residency, you will be the deciding factor. Go to the place where you can make some connections, but more importantly learn the most and be happy, because a happy medical student is a more productive one, and someday a better doctor for it, IMO.
hope this helps. good luck.