I've gotten stopped sometimes because I only use my US passport to enter the US, everywhere else I use my Australian one and so my US passport is empty. I don't like showing the Australian one to US customs because of the Cuba stamps and legally I must enter the US on my US passport.
Really, unless you are traveling between the USA and Australia, you shouldn't need to show your Australian passport anywhere. You must show your Australian passport when you enter Australia and your US one when you enter the US so it makes sense to carry both in that scenario. However, if you are going from the US to say Aruba, you really only need to carry and show your US passport.
If you are traveling to areas where Americans can travel but it may be better to show your Australian passport to the locals (like checking in at the hotel in Europe), do that because the locals may be more friendly to you as an Australian than an American. You should still use your US passport when going through immigration and customs both in the foreign country and the USA.
Really, unless you need to show your Australasian passport when entering Australia, you should use your US passport for all travel. Except perhaps when "out on the town".
ETA: It looks like you live in Australia? If so, then it is perhaps better to use your Australian passport as the primary. My example applies to a dual citizen residing in the US where most travel originates and ends in the US.
