AA miles can be used on qantas. one way 62.5K AA miles for business and 72.5K miles for first. It is very difficult to get first class on Qantas especially on the A380.

United one way is 67.5K miles for business and 80K for first.

All these are saver awards.

United usually only open up several weeks before the flights or even closer to the flight.

If you have AA miles and there is availability on Qantas, go with Qantas. Their service and planes are much more comfortable than United. If you are flying direct to Melbourne form LAX, go with Qantas on the new A380 direct LAX - MEL. Just check that they fly this plane on the day you want to travel.

Other option is using star alliance (united) miles on Air New Zealand. Very comfortable business and first. However it is very difficult getting availability form New Zealand to Melbourne. Other cities like Sydney are easier for availability.