The way I understand it, when you call someplace you're in "the Brooklyn to" some other place, you're saying everyone works over there and then comes back here at night and on weekends. While we all love to pay inordinate attention to the pampering of high-tech whiz-kid commuters, and the number of San Franciscans who work outside the city is not insignificant, the statistics belie the "Brooklyn" theory of San Francisco.
Brooklyn and Kings County are one and the same, ditto for Manhattan and New York County. According to the
Census Bureau, of the 1,071,549 workers in Kings County, some 494,455 are employed in some other county. That means 46% of employed Brooklynites leave the borough for work.
San Francisco city and county are one and the same. According to the
Census Bureau, of San Francisco County's 437,125 workers, some 94,318 of are employed in some other county. That means 21% of employed San Franciscans leave the city for work.
Again, that is not an insignificant number--but it's nothing like the numbers who flood out of Brooklyn to work elsewhere, presumably most of them in Manhattan.