Normally, by this point in these FFP comparison threads, someone has mentioned that the earn/burn ratio on AA is much better than BA. I haven't done that comparison myself, but this is readily verified. If you stick to AA, however, you will (currently) earn nothing on BA transatlantic flights (and v/v).

OTOH, the AS earn/burn ratio is also supposed to be good and presumably you would earn on AS if you fly either BA or AA transatlantic.

I guess it's safe to assume that you won't use OW enough to qualify for any kind of status? That might otherwise significantly change the equation.

Methinks it would be well worthwhile spending some time on the AS website.