Columbia is one of the best undergraduate schools in the country, and NYU is a safety school for rich kids who want to live in the city [1]. The other answers make good and correct points about specific features and drawbacks of each school, but those are all secondary to the large gap in prestige between the two schools. read more
NYU, by contrast, has more than three times the undergraduate population of Columbia, with a higher proportion of undergraduates than graduate students. Fees and funding Leading US private universities are notoriously expensive, and neither of these two top universities in New York is an exception to that rule. read more
However, Columbia is no slouch, and their graduates are more likely than NYU's to make it into graduate business schools (including the Columbia Business School, which consistently ranks higher than NYU Stern) regardless of their major. read more