Hmmm. This is a pretty open question, but I'll try to answer it (and let the AA experts add their own bits and pieces later!).
My gut feeling has always been to be in the program of the airline you fly the most. This means Qantas to me - especially due to their high local presence.
However, the AA program is actually quite good and the award flights are much "cheaper" than the Qantas equivalent flights (Keep in mind that AA and Qantas are both in OneWorld, so they have access to the same award flights, although I believe Qantas FF members have access to award flights ~30 days earlier than AA members).
You really have to analyse how much you fly and in what classes you fly. In the bigger picture, I believe that Qantas Platinum (AA ExPlat) is easier to earn with Qantas than to earn it with AA.
This of course depends on your individual flight patterns though.
Talking about Qantas Gold (or AA Plat) then especially with the "AA Challenge" it tends to be easier with AA.
If you're flying deep discount with Qantas, then you have to be careful about which class it books into. Less of a worry on higher Economy and Business fares.
With other airlines, you have to watch too. My best example of where AA is worse than Qantas is if you fly discount economy with Cathay Pacific a lot.
AA is of course free to join. Qantas does cost the $$ for Australian/NZ residents.
Don't forget the credit card angle (ie most Australian Credit Cards deposit points into Qantas, not AA. The convoluted route into AA from these cards often mean you lose a lot of points in the transfer. Same deal with Rental cars and hotels. They may want to give you less AA points than Qantas points for a transation.
Awards do tend to be cheaper both in points and "fuel fines" when redeeming with American Airlines over Qantas.
Upgrades always rely on points/status in the "home" scheme of that airline - ie you can't use AA points to upgrade a Qantas flight, and vice versa.
AA status will not give you lounge access within America (unless international flight), whereas Qantas status will.
My best advice is to look at your flying patterns, then keep in mind the earning charts at the following locations:
https://www.aa.com/apps/AAdvantage/ViewMileageProgramsDetail.jhtml?anchorEvent=false&partnerType=Air
Frequent Flyer - About the Program - Terms & Conditions
Then keep reading through the various AA vs QF posts here and make your own mind up.