I did the research when interviewing for a job in NYC.
What would cost ~3500 in SF was more like 1500-2000.
NYC has much better transit - I could commute in from Park Slope to Manhattan and have a 1500 studio which would have been much much more expensive if I say, commuted from Mission to Civic center on BART.
It is significantly cheaper if you don't live in Manhattan, and transit allows that