I think I'm likely splitting hairs but have a paid flight on J (business not first) and have the option to go either on AA or BA as the prices are about the same.

ORD - LHR out on:
BA on either 777-200, 777-300, or 787-800
AA on the 787-900 (AA Flagship)

MIA-LHR return on:
BA on A380 (my choice but this one does have a price difference)
AA on 77W

I think some years ago I would BA for sure, but now the AA J product has gotten better, or am I crazy?