I often favour BA out, AA back (ignoring the pre-departure lounges at LHR...).
For me, BA (in general) has better service, nicer food, and better drinks for a day flight. Whilst AA has a quicker service routine on the overnight (so less disturbances whilst trying to sleep) and, most importantly, individual air nozzles to ensure I'm cool enough to actually sleep! They do, however, seem to have the seatbelt sign on almost constantly so it's never clear whether you can pop to the toilet when you wake up in the middle of the night...!
For some reason I've never managed to 'gel' with the AA style of service, and feel much more comfortable on BA (again, in general - certainly had opposite experiences plenty of times!). What I've never had, however, is a truly 'good' meal on AA as opposed to plenty on BA!
The other point is that, of course, AA on the way back to LHR doesn't give you EU/UK261 protection... that's led to some additional expenses occasionally.