It depends much on your travel pattern:

Pro for QF:
- Status-Year does not reset. You may go for Plat in one year. With BA your SCs are resetted every time you reach a new level.
- Get SCs on the cheap fare buckets
- Lifetime Status

Pro for BA:
- Better burining rate

Be careful: Both need 4 Segments on QF or BA to attain/retain status.

For me QF is perfect at the moment.
I manage to get my 4 Segments on QF with one trip downunder per year.
Besides I fly short haul on BA or IB. So I clock up quite a bit of SCs.

I would not get many miles on the short hops with AA and Status is more important than a free flight.