Flying AA discount economy and accruing to AA with no status you will earn 1 RDM (redeemable miles) per mile flown

Flying AA discount economy and accruing to QF with gold status you will earn 0.875 QFF points per mile flown (discount economy on AA earns 0.5 points per mile, and your Gold status gives you a 75% bonus on that – 0.5*1.75 = 0.875)

AA is recognised as having a better earn/burn ratio than QF (though there are circumstances where QF is better – for example short haul flights in the US for only 8K points)

So accruing to AA will give you a slightly better earn rate, which combined with AA’s better burn rate means you’ll be better off accruing to AA

You should consider doing the AA Challenge to get yourself AA Platinum status – then you’ll get 100% bonus RDM, making AA even better for you

Your QF Gold status will give you AAdmiral’s Club access, even when flying domestic US – something which AAdvantage status doesn’t give. I don't think you need to be accruing to QF in order to use your QF status to get into the lounge, but I'm not certain on this point.