IME - BA First delivers a far more personalized treatment, a lot more personal space over ClubSuites, and a vastly better seat over yin-yang Club seat . If you are chasing BA tier points then the BA routing via LHR will also net you a heck of a lot more TPs.
I left AA EXP after 20+ years and have BA Gold. I have no regrets, so that BA First fare would get my attention.
As always YMMV