People ask me to compare the two countries since they both have English as the national language, have/had relations with England, are Western nations, and majority of the population is Christian (not necessarily believing). I've lived in Australia for 12 years and the US for 10 years. Here are some things I have noted:
1) Education system: I tell people that I would rather receive an education in the US than Australia. There's more emphasis on extracurricular activities, and your college/university do not rely solely on a set of exams like they do in Australia. Also, a 50% is a passing mark here, whereas in the Us, it's 60%. Higher standards in some areas. I don't like everything about the US education system, just those I mentioned.
2) Federal support: Australia offers more grants, incentives, and financial support to families and university students. I was told that the US can't do it because (a) it pumps a lot of money into its military and (b) Australia's population is barely 20 million, compared to the 300(?) million in the US. Also, Australia encourages families in order to increase its population, so it's more accepting of immigrants (who can prove that they are attending a vocational course upon entry).
3) Australia seems to be the midway point between American and European culture. Guys here to dress differently. They style their hair and wear brighter colors (I'm talking neons). Also, I've come across more older people who dress like teens (hair dyed pink and all).
4) Australia is definitely more accepting of ethnic communities, and you can feel it in the air. I have yet to meet an American who has visited Australia and said otherwise. 50 years back, Australia was different story, so acceptance is more of a recent thing.
5) Prices: Besides the stuff you find in dollar stores, a lot of things are more expensive in Australia. Australia is more of an import economy, so far from the rest of the world. Gone are the days I could use a dollar to buy a chocolate bar. A dollar gets you little to nothing here. (While on the topic of chocolate, Hersheys is blegh. I am glad I moved here. More Cadbury, but no Twizzlers.)
6) Australia seem less conservative. There are massive billboards with only the words, "WANT LONGER LASTING SEX? Call XXXXXX" on main roads, and they stay up there for quite a while. If this was in the US, that billboard wouldn't last the week. I read a study that compared 18 years olds in the US and Australia, and Australia had a higher percentage of youth stating that they were atheist or had no religion
7) Fewer amusements parks in Australia
8) The more I travel, the more everyplace looks the same. Roads, markets, parks. The main thing that makes me realize I'm in Australia are the trees and some of the stronger accents.
9) America=cool to Australians. When people hear me speak, they want to hear more. The American(ish) accent worked wonders when I was teaching. Students were mesmerized. Even the ones I weren't teaching would come to my class just to hear me speak. Oddly, people ask me if I'm Canadian. I guess because I've lived in both Australia and the US during my developmental years, I've got a bit of both accents, hence making me sound Canadian(?). I mean, what do Canadians sounds like? I've never paid much attention. Sometimes, they laugh at the Canadians here, not in an rude way, but teasingly.
10) Vanilla ice cream, honey, and ketchup taste better here.
I've lived in Sydney and Melbourne, and New York and Boston, so my perceptions are limited.
Maybe someone should compare the US to Canada or England.