I had a really awful expereince with AA the other day in terms of crew quality (ground staff at both ends and cabin crew). That said, it was tolerable because of MCE seats.
If you have status I would say AA out and BA back (due to lounge quality in LHR T3 vs T5, and MCE if in economy), but it sounds like you don't. So at this moment in time would recommend BA.

Also (something I just realised) you are only covered by UK261 in terms of delay compensation etc outbound on AA (as a non-UK operator) but both ways on BA.