The Qantas Frequent Flyer is a good second program to belong to if your primary program is with AA. Considering:

1) Earning 100% miles on just about all discounted Y fares
2) Mileage for BA transatlantic
3) 1000 mile minimum for QF flights (and I think this might be expanded to AA & BA)
4) Free Qantas Club membership if you reach Gold or Platinum - which will give you free access to AA's Admirals Club (granted you have to fly a lot on both AA & QF for this benefit to be of value)
5) Access to BA transatlantic awards - even Concorde!

Up to now I've logged all my flights with AA (averaging 200K flight miles per year for the last 4 years). This year I joined QF's program and will be putting enough flights with them so that I will reach Gold and get the benefit of Admirals club access. BA transatlantic earning (and award redemption) is my second reason.

Even if you don't reach Gold with QF you can buy a Qantas Club membership for a lot less than an Admirals Club membership, so that may be a good enough reason to join QF's program and just put a few flights with them.