If you only fly (even severely discounted) business class, you will hit EXP and earn 4 SWUs after just 50,000 miles (every mile flown in premium cabins earns 2 EQM per mile now with the 2016 changes). At 75,000 miles you'll earn another two, and at 100k miles another two for a total of 8.
Looking just at this aspect , AA comes out ahead of BA here.

HOWEVER, I see several issues why AA might not be the best program for you. First, AAdvantage SWUs are only usable on AA metal flights on AA tickets. Not all good BA deals like the DUB fares are necessarily found on AA as well.
Then, keep in mind that AA is in the process of removing its F cabin on all aircraft except the few (13?) 77W frames they have. Those service LHR-JFK only (from the routes you mentioned), and you will not be able to use your upgrades on any other route as there wont be a cabin to upgrade into. BA offers F on way more routes, and you'll be able to upgrade all your longhaul flights using BAEC instruments.
Also, AA will move redeemable miles earning from distance-based to spend-based later in 2016. This will greatly and negatively affect those who buy heavily discounted premium cabin longhaul flights. Example: FRA-FDW-GRU and back right now nets 41,000 redeemable miles before any bonuses as an EXP, but that will be reduced to ~15,000 miles after the move to spend-based earning if the ticket cost just $1,500 - as an EXP you'll earn 11 times what you paid for the ticket (minus certain taxes). Also, AA charges co-pays for upgrades when using miles.
Even with the 2015 devaluation, upgrading with Avios remains one of the sweet spots of BAs program.

My advice would be to stick with BA for this year and see how AAdvantage will evolve, especially how upgrades will get handled with the introduction of PE, before deciding on a switch.