Hi Webup -
I have experienced your exact situation and handled it in the following way:
I lived in the US, was an AA frequent flier and moved to the UK for a stint. Usually flew economy fares. I found very quickly that when flying on BA, you usually only got 25% of miles flown (and 0% on flights between the US and UK). Therefore, I moved to BA, ended up getting 100% mile accruals and rewards within Europe for relatively "cheap" burn rates. Also, just attaining BA Silver ended up getting me several complimentary upgrades from economy to business (bypassing premium economy)
I then was presented with the opportunity to go to Australia for a couple of years. I thought, hey I had to go with BA in the UK, so I better go with QF in OZ. I signed up for a QF account (with my UK address so free of charge), as I was wanting upgrades on flights from the UK to OZ or OZ to US and vice versa. This is the ONLY way to get upgrades. Well, I found out very quickly that after 3 R-T economy flights I still couldn't get Qantas Gold! (Which meant no free lounge access and I was behind everyone in the upgrade queue and seating assignment queue!) I also found out that the "burn" rates on Quantas were TERRIBLE! (16k just for Sydney to Melbourne economy, 36k Sydney to Perth or Auckland economy).
After doing a bit of research, I fired up my old AA account. Guess what, after 2 round-trips I was an American Platinum member! (Equivalent to Qantas Gold - American Executive Platinum is their top level). You must be careful with challenges, generally there have to be on AA metal ONLY - so I did it the "long" way using QF metal (AA doesn't fly Sydney to London). The big tip that those on the AA board gave me is that AA doesn't enforce the 4 flights on AA metal rule if you have over 50,000 miles accrued. Now, I don't have the opportunity to upgrade on Qantas - but you need a lot of miles to do that. However, I do get access to all the Qantas lounges, even when flying Sydney to Melbourne. I get "preferential" seats on Qantas planes and can book a seat when I book my ticket. The BIG advantage - I get rewards on Qantas (using AA reservations) - 20k for ANY R-T flight within Australia or to New Zealand (in economy) or better yet, 35k for BUSINESS!
I guess it all depends what is important to you. If you want to upgrade using miles (assuming you will accrue enough to do so) QF is the only way on QF flights. However, keep in mind that if you are a Bronze or Silver QF member, your chances are slim. If you can't attain at least Gold, you won't get lounge access when flying economy. You won't get "preferential" seats either. And the "earn" and "burn" ratios are definitely weighted in QF's favour.
However, if you want lounge access when flying QF anytime, preferential seats, great earn and burn ratios - and if you are ever flying within the US on AA you will also get several complimentary upgrades - go for the AA membership and do all you can to attain Platnium quickly!
(As stated above, you will want to ensure that you are flying in at least QF economy classes H, K, B, or Y with an AA membership)