Comparing the accident numbers between the USA and OZ is a little hard. You have to take a few things into account and I did a detailed comparison to compare like for like a few years ago but there has been new data since then and I haven't repeated the exercise.
1. The LSA(not not the Part 103 ultralights) figures will be incorporated into the NTSB figures. The ATSB separates out the RAAUS numbers.
2. At one time one of the agencies was reporting fatalities vs fatal accidents. Ie if 4 people were killed in one accident one counted it as 4 while the other would count it as 1. I cant remember which way round it was and I think that in newer reports the reporting has been changed and they now align.
When I looked it wasn't the factor of 3 that is often quoted but there was still quite a difference with the USA being safer. What makes it all the more amazing is when you look at the things they are allowed to do that we either need additional training for or are prohibited.
eg. Night VFR without a separate rating, No rating required for formation flight, No extra training needed for low level flight. No requirement for an aerobatic rating.
Also amazing when you think about how often they land their little Cessna on runways covered with snow and ice and how if you are above 7,300 feet in Australia it is impossible to have a CFIT incident. Also add to it the fact that in the USA you dont need a clearance to fly VFR through class C (just be in contact with ATC) , dont need a transponder in class E, there is no requirement to wear a lifejacket on a single engine private flight. How come their accident rate isnt so much worse?