Australia does provide public housing, but I'll take a stab and say it's cut back from its peak amount.
When you travel through California (and the US in general), i'd estimate homelessness and poverty to be at least an order of magnitude worse in the US (I want to hesitate to say two orders of magnitude worse) compared to anything I see at home. Clearly there's something about society and/or the structure of social safety nets that has a real and measurable effect on poverty and homelessness overall.
/ before someone jumps onto Google to try to disprove me: I've been to both countries (several times in fact), and worked with both homelessness and official national statistics. One of the things internet pundits misunderstand is the definition and measures of homelessness/poverty between the two countries: I think my estimate is pretty fair napkin math, it might be a 4 or 5 multiple instead, but I think we're quibbling by that point.