I would argue that Columbia has a nicer campus (i dont really consider NYU as having a "campus"). I think NYU is known for a legacy of big name filmmakers back when film schools were the big thing for the film industry. Lately Columbia has been more successful in having successful alumni.
NYU has better facilities (from what I hear), Columbia's are disappointing (they have 2 cramped editing bays and a very small space in general). If you go to NYU you would probably get a better technical understanding of film. At Columbia its more about screenwriting/crafting developing ideas as a writer or director. Columbia puts a premium on this (thats why you can only shoot digital for the first year(s).
I saw the short doc series "Film School" which features NYU and it really disappointed me. When I saw how the faculty communicated with the students about their work they focused on their emotional reaction and were not able to discern the technical problems with students' work (problems with their story structure, characters, etc). Also, the students couldn't get their emotions in control. But hey, it was a reality show (lol...it just bothered me). BTW, you can get that series through Netflix.
Miriam May, can you please let us know how your visit to that Columbia class turns out??
"I put my heart and my soul into my work, and have lost my mind in the process." Vincent Van Gogh