If travelling in premium cabins, then QF gives away status like candy
If travelling in economy, AA can be a lot easier to attain status , especially if based out of AU where only Y is eligable for full SC earning

e.g. if based in LA and flying to JFK

< K class ( assuming eligable for earning miles ) , would earn approx 1236 miles and 20 SCs
If K or higher ( other than Y ) would earn 1275 miles and 20 SCs
Y class would earn 1275 miles and 40 SCs

Attaining Silver status (other than in full Y) would require 18 sectors

If crediting to AA, would earn 2475 qualifying miles in economy ( other than B or Y class ) and so need 10 sectors to attain the equivalent AA status

for those on B or Y class, AA does have a higher qpoint earning that would mean that a B class traveller would only need 7 sectors

On a LAX-SYD run in economy ( other than Y ) would earn 45 status credits so 8 sectors needed for QF silver. Crediting to AA would count 7488 miles of the 25000 needed which is just under 1/3 of the status requirement

QFs scheme is very heavily weighted to getting status to those travelling in premium cabins, whilst AA is slightly weighted to premium cabin

If based in the USA, there are other benefits for the OP to credit to AA.

Not all AA fares will be eligable for miles earning at all to QF whereas v few AA issued fares will be ineligable for AA miles
with status on AA, will be able to use electronic upgrade credits to upgrade from cheap economy to 1st
With status on AA will be able to pre-select exit row seats on AA
Redemption rates are typically much lower

Drawback is that QF Gold status ( if attained ) would allow access to AA lounges for domestic travel whilst with AA Platinum would need to purchase a lounge membership

Dave