I recently had a chance to compare the two J products, flying SFO-JFK-LHR-JNB-LHR-JFK, with the transatlantic on AA and the flights to and from JNB on BA. BA's J seats are far superior and much more private, and the food, service and AVOD are better as well. But the transatlantic are relatively short interncontinental hops.

For me personally, the decision would hinge on whether I thought the AA EQMs would help me qualify for higher status on AA and whether I thought I'd be sleeping most of the way (since if I'm sleeping the seat quality actually means less to me). If one or both apply, I'd definitely pick AA. If not, I'd do BA, enjoy the better seat and other stuff, and start accruing some miles on its program.

Oops! Now that I've given you the full benefit (??) or my wisdom (?????), I just remembered that AA is offering double miles for travel to LHR booked and completed by Dec. 15 and a free companion ticket for JFK (and LAX) travel to and from LHR. Not sure if you'll be flying this soon or if these deals apply to LHR-JFK-LHR (as opposed to vice versa), but thought I'd mention them.