I have not done longhaul 380 but from what I've heard / read and from what I know about the BA CW product, AA's new J on the 77W (773) beats BA.
I've done it recently and the seat is great in terms of space to sleep and personal space in general (no climbing over your neighbour etc).
For me, an ideal seat on the UD (62A / K, 64A / K) would be strong competition for the AA 77W but I would on balance go AA over BA CW (as said, not flown 380 longhaul (did a training flight to FRA in CW and F)).