Discount Y flights on BA will only earn 0.25 points per miles in the QFF program. As you mention that BA flights will only be to Europe, then this is not a great milage earner anyway.

Certainly the bulk of your miles are going to earned between UK and AU. Flying BA or QF on this route will earn 1 point per mile regardless of the Y class.

Flying AA between UK and USA you would earn 0.5 points per mile if crediting to QF.

QF flights credited to AA would only earn 0.5 points per mile in discount Y.

So a toss up between QF and AA. QF would earn you more miles than AA, but QF awards are typically more expensive than AA (miles + taxes)