QANTAS most likely.

Because if you take a mixture of BA and AA flights, you can't really stick with either one of their programmes as they don't allow you to accrue mileage on the others' transatlantic flights. On QF's programme you do.

BA's inter-European flights don't earn very much miles due to the fare. SO check out your fares carefully before you buy. QF is also FFP partners with SWISS, and ALITALIA in Europe in addition to other ONeworld members as well.