According to the 2011 American Community Survey estimates, which seem to be the latest Census Bureau data available on this topic, median gross rents are:
San Francisco - $1,407
New York County (i.e. Manhattan) - $1,403
Washington, DC - $1,216
New York City as a whole - $1,168
It's a good thing that people in this thread are making the reasonable comparison of San Francisco to Manhattan and not the absurd comparison of San Francisco to New York. train makes a salient point about rent control; I know a number of people living in San Francisco on far less money than one might expect, but for a new arrival the only remotely reasonable place in terms of housing is out in the Sunset, which is far from everything and in terms of weather is basically Alaska.