for the 5 years i was living in the EU, it always seemed to make the most sense to travel on the passport of the place i was arriving... so when going to the EU I would use my irish passport and when going to the USA i would use my US passport. The one time I goofed and used both in one journey it caused confusion and I ended up having to produce the other one anyway.

definitely use your AU one when you leave the USA, regardless of which you use to enter the USA. A resident going home has fewer hoops to jump through.