Putting aside the option (and hassle?) of your DUB routing, AA is much better on LHR-JFK-LHR than BA, mainly due to it's 1-2-1 seating on its 77W planes that it uses exclusively on this route. So the seats are roomier, more private, have better IFE and afford you all-aisle access. The only downside is that AA FAs can be more hit and miss than those of BA, but not to the extent that it would sway my decision under these circumstances.

As for your lounge question, don't you have access to BA lounges while flying AA in business class, whether by virtue of their One World partnership or your BA Executive Club membership...or something like that?

Back to the DUB option: Can't find the link right now, but I believe that recently BA made noises about cracking down (probably by suspending or terminating BAEC membership and Avios points) on passengers not taking the last leg of a flight (for you, skipping LHR-DUB). Whether it would even do so, especially if you did this just once, is unlikely. But you might check further into this - say, at the BA forum - before going that route.