See my comment above - I think some posters have been repeating the "traditional wisdom" of using BA (over AA) for Eastbound overnight TATL flights...but to my mind the only cases that makes sense is on the short East Coast routes where BA offer a true "sleeper service". There is no "sleeper service" on either MIA or DFW on BA; and on AA the "express meal" option is very quick, plus the seats in J are very private so with an eye mask you can sleep even if other passengers are still dining.
So for this route, I'd still say AA Eastbound as well in J since the seat is better for sleeping than BA (in my view). The new AA arrivals lounge in Terminal 3 is also just as good as the BA one in T5 - good showers and decent breakfast, even if the room is a little smaller.