I don't think that SF is better than NYC for the homeless.
A big difference between SF and NYC is that NYC provides shelter for people that can't afford housing and SF does not. Only 5% of homeless people in NYC are unsheltered compared with 67% in the Bay Area.
Legally, NYC is required to provide shelters for anyone who needs it, while SF shelters have waitlists of over a month.
I have no idea, but a lot of non-profits around the Tenderloin provide services to the homeless that might be harder to capture. There's also less urgency to shelter because it doesn't freeze.