I would choose AA if you decide on PE. AA does not charge for seat selection in PE. I am also 6' 4" and I think there is more room in AA's seat, largely to do with the footrest configuration. BA's 773 front row is at a bulkhead and while there is plenty of knee room you can't stretch your feet out. AA's 773 (77W) front row is at an exit and the window pairs have endless leg room.

In economy you will have to pay for seat selection on AA as well to get anything good. It may be worth it though as AA has its MCE rows with extra pitch.


EDIT from a service point of view, I'd go for BA.