No, San Francisco covers a much smaller land area than NYC; it's subways are all east of the neighborhood known as "West Portal," at the western exit of the Twin Peaks Tunnel. The rest of the city has extensive electric rail and trolley (electric) bus coverage. There are diesel busses too but they don't work as well on the hills as the trolley busses do.
When I was growing up, the famous cable cars were considered to be just another part of the mass transit system but they're strictly for the tourists now.