Some good advice already provided above. Like most things, there are pluses and minuses - but as someone who lives in Oz, I wouldn't dream of switching from AA to QF.

The earn and burn rates on AA are generally far better than on QF. For example, I booked MEL-CNS-MEL in J (U) yesterday for my daughter - 35k AA miles -- QF wants 72k for the same ticket.

Anytime awards on AA - which I've never used - but at twice the miles of a Milesaver award, they're not bad, particularly as they book into full fare inventory so if the seat is there, it's yours. QF recently introduced similar types of awards -- at utterly ludicrous mileage requirements.

Availability of OZ-US tickets in business. As Dave Noble said, easier if you're a QF member because QF uses Amadeus and the inventory is loaded 355 days out, whereas AA uses Sabre and the inventory is only loaded 330 days out, so QF members effectively have a 25 day head start.

QF Platinum (= AA EXP) get complimentary QP membership. AA EXP doesn't even get you into an Admirals Club (on a domestic itinerary).

QF Platinum - get to call their equivalent of the EXP line; if you're AA, you have to make do with the general number (though in my experience, that's never been a major issue -- and I got a superb QF international agent the other day when I needed help straightening out a RTW ticket).

As Dave Noble points out, if you stick with AA, you have to watch out for non-mileage earning QF tickets. Some will only earn 50% miles and some 0 miles. Annoyingly, the QF website doesn't tell you the ticket inventory until after you've bought it (unless you want to try and decipher the source code of the web page).

Much of our flying is to/from the US and to the UK and then back around Asia etc., so I've found it much better to stick with AA than switch to QF. The amount of strictly-Oz flying we do is limited - compared with the US, there just aren't that many places to fly to! The downside is (if you're AA) there's no way to upgrade domestic Oz (or international) QF flights, as you need QF points to do that.