In general Australia has a lower crime rate than USA. Of course, there are absolutely areas within USA that would have a lower crime rate than certain areas of Australia.
- Health Care
Australia has well established free public health care that covers general illness, radiology, necessary surgeries, disabilities etc. Higher income earners are expected to also have private health insurance and are penalised in their taxes if they don't have it. However, if you're a low(er) income earner or simply prefer the public health system it works quite well.
There's also a pretty solid Welfare system if you are worried about income stability for whatever reason.
The free public education system is also quite good, although I'm unclear on how it compares to the USA.
Of course, there are also many benefits to living in the USA over Australia - particularly if you're working in the tech sector. There is a strong tech scene in Australian capital cities, but it's fairly quiet elsewhere. There's nothing comparable to Silicon Valley.
Depending on your business, the USA can also be a better place to start your own business - larger sales capacity (if you can deal with the fact States have very different taxation rules etc.) and significantly more VC opportunities (although Australia is slowly picking up its game).
Film and TV industries are also obviously miles behind LA or even New York. So if that's an industry you're interested in then USA is the place to be.
However, Australia seems to compare fairly favourably when raising a family is your biggest priority, say over career advancement.
I also feel like there was more pressure to "keep up with the Joneses" in SoCal. Mind you, I live in Newcastle, so I kinda avoid the housing problem that we have in Sydney and (now) Melbourne.
Also, foreigners that move here after the age of 35! We have private health cover as well and it's great.