If you're looking to obtain status, bear in mine you'll need 4x flights with the FF programme operating carrier - so 4x BA coded flights or 4x AA/US coded flights for BA/AA status respectively.
I'm a member of both, and they both have pros and cons. AA is better if flying discount Y (100% EQM earning) and for LH redemptions, BA is better for SH redemptions.
The main reason I'm doing the opposite (switching from AA to BA) is that I can't commit to the 4x AA/US flights each year any more, but can do so with BA no problem.