Regarding the comments about service and crew quality, I think it's honestly a crapshoot. Both AA and BA are big, and in my experience it really depends on who you get as crew.
I'll admit that I've flown AA a lot more than BA in recent years, but to say that between these two airlines that one is consistently good and the other consistently bad is a stretch.
One area where I find AA to be consistently better is connectivity. Last time I flew BA in 2022 was LHR-BWI on a 788 with no WiFi. I did later see in the fine print that the 788s weren't WiFi-equipped at the time, but by 2022 I had come to expect it as standard on a transatlantic full-service carrier.