When I worked for the public defender, most of my clients were homeless at some point.
They were homeless, and mentally ill, because they chose to use powerful, mind-altering drugs that fucked up their brains. They chose to keep using those drugs.
I have absolutely no sympathy for drug addicts. Using drugs is a choice. The fact that it has serious consequences does not engender sympathy. If anything, the fact that people know drugs will fuck them up and still use them anyway makes me less sympathetic to drug addicts.
I have great sympathy for the homeless who are merely down on their luck. You can identify them pretty easily. They're the ones that aren't drunk or high, and they're usually in the shelters at night because they'd rather have a hot shower and a hot meal than spend a night on the street with the addicts.