I would choose the AA seat in a heartbeat. I don't particularly enjoy the BA soft product, but you're really buying PE for the seat. And in that aspect, AA is the clear winner.
Another thing to note if you're buying your ticket yourself (as opposed to an employer-funded ticket). If you don't have OneWorld elite status and want to select a seat prior to check-in, you'll have to add a hefty sum to the cost of the BA flight.