Excellent answer.

Only other thing I'd point out is something I think most of this thread is ignoring:

There's a difference between homeless and panhandler.

Homeless is someone who literally has no home. Identifiable by the fact they've basically got everything with them. The ones with a bunch of bags or shopping carts. Occupying the end of a subway car, or a whole bench surrounded by crap. Despite some of them looking like hoarders or offensive smells, that's hardly universal. Some look like tourists with a few suitcases. Groomed and everything.

There's also people who just panhandle. They might be on disability, social security, or live with family. They just need money for their vices. Gambling, alcohol, whatever. They generally will be dressed seasonably and not have belongings with them. They've got a place for them. They're just looking for spending money.

These are two distinct groups with different needs. NYC is especially more hospitable to panhandlers than NJ. Foot traffic and all. Much more tolerant, and much more opportunity.

I'd argue for most, NJ is slightly more hospitable to homeless. A ton of homeless people in NJ (and in much of the US) live in their car parking in places like Walmart, largely unnoticed. While hardly great, lets be honest it's safer than many shelters, and protects them from the elements. It also gives them some degree of privacy. I suspect that's the preferred route when possible in NJ for people who lose their home.