If you book AA flight numbers then you will earn AA miles/LP's based on the fare. If you don't have status that will be 5 miles/LP per dollar (not including taxes).
If you book QR flight numbers then you earn miles/LP's based on distance and booking code according to the table at aa.com below.
So you just have to do the math and see what will earn you more.
AA.com - QR Earning