It may be a no-brainer for travel at the back of the b*s, but for premium cabin travel the choice is much closer. In fact, for a daytime flight in business class, I would be taking AA over BA as I find their seats more comfortable for sitting. But for a night flight, I would select BA if confined to business class cabin.
But now that I have some AA candy to collect (just as soon as they post my QF flight from yesterday), I would be looking at the option to move into F on AA rather than confined to J on BA.
However, as this thread was asking about economy travel, there are a few things to note. AA seat pitch is better, but IFE is very poor. AA does have in-seat power throughout the economy cabin (not every seat, so select sear carefully) and BA does not. So if you want to use a laptop during the flight then AA is better.
FF earning on the QF program is also affected by the fare basis purchased. Many fares will only earn 25% mileage on BA but will earn 50% on AA. OneWorld Explorer and Global Explorer fares book into L class and this is going to earn better on AA than BA.
So when it comes to IFE, service, food, drinks etc, then BA wins. When it comes to in-seat power, FF earning (on QF or AA program), then AA wins. Which is more important to you will depend on your personal situation and preference.