I'd go through ORD because I'd rather the shorter (3.5hr not 5hr, and longer on the return) domestic F than the better lounge. Definitely not MIA though. Plus I'm a fan of Dreamliners in general, not that I've flown the 788.
Being PHX based I've flown the BA product several times and wouldn't do it with AA metal available. I will admit the evening departure and longest lay-flat time is nice, but the AA business class is nicer and you will get into BCN earlier.