Interestingly, by law New York City must provide shelter to anyone in the city who is homeless, qualifies for relief and requests shelter. So it's not just that city government happens to be more supportive of its social services programs, there's an actual legal obligation to shelter everyone (and they can, and have been, sued if they don't meet that obligation).

https://www.coalitionforthehomeless.org/our-programs/advocac...