For full disclosure, my opinion is pretty biased because I went to UMich and took lots of classes in the engineering school, and my opinion of UNC comes from family members who attended there.
Michigan Engineering is ranked #6 in the US, UNC #93. The big difference at UMich is that nearly every program is ranking in the top 10, only chemical engineering is less at #12. This gives you a lot of flexibility to switch between programs; any one you decide on will be good and most students change their interests. You can also dual-enroll at LSA or the Ross business school (ranked #4), this a pretty popular option too.
There is a very large international student body on North Campus from pretty much everywhere ; lots of Chinese, Koreans, Indians, S. Americans and even a few Europeans - especially as engineering graduate students. UNC has fewer internationals and fewer OOS domestic students, I believe that Michigan residents are 62% of the freshman, at UNC is is around 80%. There are significantly more women than men at UNC: 59% of the UNC freshman class is female, at UMich it is closer to 50-50.
The quality of the professors and students at both schools is extremely high. UMich has a higher mean and smaller range of ACT scores. The UMich engineering school is predominantly male (about 70%) and has a higher ACT (average:33) than the remainder of the university.
In my experience, the UMich engineering school is designed to help you succeed - there are departmental lounges where you can get tutoring and help all day, lots and lots of office hours and review sessions, and an open door policy for administration. If you want to have a chat with the dean, just make an appointment! In addition, there are incubators and a department to help students start businesses and a thriving startup community. The computing resources are world class with labs open for student use 24x7. Successful graduates often come back and lecture on the companies they started. There are lots of student teams - the most famous being the solar car team with has won numerous awards (latest: Abu Dhabi solar car challenge) Recruiting or UM grads is pretty fierce, most students have several job offers by the time they graduate.
Campus wise, both are very nice college / research towns, with Ann Arbor the quintessential small college town (population 113K, regional population 344K) and UNC in a large city (Chapel Hill, population 59K, regional population 2 million) but contiguous to Raleigh/Durham). Ann Arbor is much colder, with snow a few months of the year but lots of winter sports. Lots of great, affordable restaurants in both places even on a student budget. Ann Arbor is rated the #1 most educated city in the USA, Raleigh #10
Tuition at UMich is higher: currently appx USD 43000 per 2 semesters vs 34000 at UNC. Very large difference, especially considering the low A$. There are also a number of engineering scholarships like Stamps and Shipmans; you should check the engineering web site for contact to see what is available to internationals. You can apply for need based aid after 1 semester.
http://www.engin.umich.edu/college/admissions/finances/scholarships/international
UMich has one of the best swimming and diving programs in the USA. Michael Phelps trained in Ann Arbor for years, and Michigan has produced many Olympic quality divers and swimmers. If you are competitive at the state or national level, or close to it, I would urge you to contact the athletic department at UMich. You probably won’t be on their radar as an Australian, but as a recruited athlete you could get a partial or full scholarship. If not, it might be interested to go to the meets.
Both are large state schools and have their share of partying, but not so much on the North Campus at UMich, which houses engineering, CS, music, design, art and architecture. Ann Arbor has a pretty amazing sports culture with everything from football to cricket on a sponsored , inter-mural or club level. I’d also give the edge to Ann Arbor for things to do : largest art fair in the USA in the summer (500K people attend) , amazing concerts and music with cheap student tickets ($10-15 usually), (even Kasey Chambers stops here on tour) , tons of free student concerts and lectures, free transportation on university and city buses too. The airport is Detroit (DTW) appx 35 min away, $15 shuttle to campus) but unfortunately there are no non-stops to Sydney.