What is the source of your data?
Wikipedia, using data from the  United Nations Office on Drugs and Crime  give figures for homicide rates per 100,000 population of 0.98 (Australia, 2015) and 4.88 (US, 2015).

And there are easy to find critiques online of trying to compare general categories such as "violent crimes" because the definitions of violent crime in different countries are different. You might want to also look at the SNOPES examination of the meme that Australia's violent crime rate increased after their gun ban in the early 1990s. That claim has been pretty thoroughly debunked. 


In terms of firearm (gun) related death rate per 100,000 population, Wikipedia reports rates of 1.93 (Australia, 2013) and 10.54 (US, 2014). In other words the US rate of gun related deaths is over 5 times higher in the US. And since I expect you'll post something about suicide, the comparative rates for gun-related suicide deaths are 0.74 (Australia, 2013) and 6.69 (US, 2014).