I had this same question for a trip in May and opted for BA. The decision was made easier since BA is now in the same terminal as AA. Previously if you came into JFK on an AA domestic flight it was a pain to transfer terminals. It's really a tossup now, since you have access to the same lounge in JFK and BA is (in theory) running all Club Suites between JFK and LHR. I actually prefer the J seat on the AA 777-300, and I think the chances of an SWU upgrade to F are a bit better on AA, but we opted for BA because the schedule made more sense.

I would not fly on any BA flight with the old Club seats.

Regarding "wasting" SWUs on an F upgrade between JFK and LHR, what better ways do you realistically have to use the SWUs these days? Some domestic itinerary that you'd probably get a complimentary upgrade on anyway? The incredibly elusive Y->J upgrade on an international flight?