I would say that, as far as academic pathology training programs are concerned, Cornell and Columbia stand out among the rest of the NYC programs, both in terms of reputation and quality of training. But, of course, I am biased.
Between Cornell and Columbia the comparison is an ongoing debate: they are both very similar in terms of size of residency programs, volume of surgical specimens and academic vs. private practice aspirations of their graduates. They are both fairly visible in the publishing (journal articles, books, etc.), academic meeting (e.g USCAP) and consultation domains. Also, there is significant exchange in fellowships and junior attending positions (meaning they hire each other's graduates) and they are part of the same hospital!
Individual strengths, however, differ: Cornell is better known for breast (Dr. Rosen), hematopathology, cytology and dermatopathology and it is stronger in CP. Columbia is better known for renal pathology, neuropathology, soft tissue and autopsy and has stronger research support (if you don't count the Cornell-Rockefeller-Sloan Kettering connection). GI and GYN are probably similarly strong. Finally, the individual "feel" of each program might be different, but that is best experienced and evaluated when you physically visit, e.g. for an interview.