If I was paying for FC and had the choice of a BA bed or an AA coffin? No question, I'd fly BA.
But the special deals AA offers to corporates (either fare discounts or guaranteed upgrades) coupled with the widespread availability of VIP and mileage upgrades mean that you're not really comparing like with like.
I also feel a sense of loyalty to AA because they treat their best customers really well. I am currently noth EXP on American and have a BA Gold card. I would always prefer to push my travel dollar in AA's direction rather than BA's.