I'm from NY and applied to all the NYC ophtho programs, so I can offer my humble observations on the matter.
I don't know that much about Columbia's program. It's kind of small (only 3 residents per year, covering one of the largest and busiest hospitals in New York), so the residents are busy. I think the program compares pretty evenly with Cornell's.
New York Eye and Ear is an excellent program. The surgical volume there is realtively high, and the clinics are busy. The residents work very hard, and they are the only NYC program that I know of that has almost a full day of general clinic on Saturdays. While it lacks the Ivy league status that Columbia and Cornell share, I think that many ophthalmologists will agree that NYEE is the best of the three.
Manhattan Eye and Ear used to be an independant hospital and residency program (and a very prestigious one for that matter). A few years ago, the hospital faced serious financial and political problems and almost shut down. In the end, however, the hospital was taken over by Lennox Hill Hospital and the residency program merged with NYU's ophtho residency. It remains an excellent program.