Hey Glenn,
I have only applied to Columbia as a MFA film school and I want to be a producer.
I guess my admiration for Columbia derives from the fact that it does have an incredible focus on the stories and the development of the stories. There is this great exchange between film theory and practice and you can get lots of inspirations from the faculty. They have a great emphasis on narratives and the faculty members, beside being very academic, they have lots of awards from every kind of film festivals.
NYU on the other hand, probably, in terms of technology and art of cinematography might still be unbeatable. They believe that students learn mostly in practice. The students don't have much time to work on conceptual part of cinema in their classes.(or at least they said so)Probably, NYU is better in directing.
These are the things that I learned through listenting to former NYU and Columbia students. But maybe I am wrong.
BTW, I heard that Columbia really wants their students to be a real storyteller - and be involved in screenwriting, directing and producing.But I heard that, their strongest department is screenwriting.
I did not really check out the NYU website but as someone who wants to tell lots of stories, I love Columbia!
So I guess,in a very simplistic way, I can say:
NYU kids are great filmmakers
Columbia people are great storytellers.
I hope I did make sense to you.
good luck and take care