This is a pretty variable part too, perhaps even more important than the actual "official" level of benefits. One of the bigger differences I've noticed moving from the U.S. to Denmark is not so much that the social welfare system is more generous (though that's true also), but especially that it's more proactive and less bureaucratic. If someone mentally ill is in need of support, qualifies for it, and cannot navigate the system themselves, a social worker will help them out. If they need somewhere to live and can't rent their own apartment, they'll get helped out there too. Someone will literally rent them an apartment, take them to it, make sure they settle in, and then check back later.
In the U.S., none of that is true. I have some pretty recent experience with an American uncle who has advanced M.S. and has gotten basically no useful support. For a while he was unable to live alone, but officially the government didn't give a shit, so he did anyway, and injured himself regularly. He alternated between living in his apartment for a few weeks at a time, and ending up in the emergency room several times per month each time he injured himself. You might think: at this point, shouldn't he move to an assisted-living facility? It'd actually be more cost-effective, but nope, neither SSI Disability nor Medicare Disability cover that. SSI Disability will pay his rent to live at home, and Medicare Disability will pay his hospital visits, but neither will pay for him to move to somewhere that makes more sense.
He would probably have ended up homeless or dead if some family members hadn't agreed to take over power of attorney, navigate the system on his behalf, and find money to pay for his rent. The U.S.'s joke of a stingy social system surely hasn't done anything on that front.