SF and NYC used to be fairly comparable as far as cost of living goes but now renting in SF is comparable to a dozen other metros (eg. $3k for a 1 bed, under $4k for a 2 bed) but in NYC it's a now an absurdly expensive outlier eg. $5k+ for a 1 bed in a convenient area in Manhattan or Brooklyn.
Beyond that eating out/going out/uber+taxis all seemed much more expensive in NYC than SF when I visited last month.