There are certainly drawbacks to attending an NYU/Columbia-type MA program. There may also be advantages, depending on the background of the student. I suggest that OP reach out to current MA students at both departments to learn more about each program.
The previous commenters referred to NYU as an unfunded program. I know from experience that for some people it can be a funded program. This funding may or may not be enough to justify going to NYU, but it is funding nonetheless.
OP: If you talk to the students in the program and you like what you hear, go ahead and apply. If you get in and you don't like their funding offer, then you can go a different route. In general, be wary of this forum, as it is filled with false assumptions and misinformation. The best source of information will usually be students in the department.