If you think you have a chance at making EXP (and remember, even cheap WT+ fares earn 1.5 EQP/mile) then AA has some advantages when you're on AA metal; you'll get the 8 SWU upgrades and free domestic US upgrades (plus much better domestic US mileage upgrade uptions).
However, you cannot upgrade cheap WT+ fares with AA miles, though you can with BA miles. You'll also have lounge access on all domestic US itineraries with BA status. Also, if you fly to Asia you'll be able to use your carrier's metal if you're with BA and hence can upgrade with miles while the only way to do this with AA miles is on exorbitantly expensive fares.
Perhaps let us know a little more about your travel patterns (portion domestic US, portion intercontinental)?