To the original question: I'd say very tentatively yes.
I ran the numbers for a friend a while back, who travels mostly paid J or F, often full fare, and he would be better off with BA. Meaning, he would get a higher status more quickly with BAEC than with AAdvantage. Now with the recent AAdvantage changes that give 2 or 3 EQMs for business and first, it's now slightly less clear, but he still comes out ahead, meaning BA Gold (OW Emerald) versus AA Plat (OW Sapphire). The question is, though, if the redeemable benefits are better. BAEC has some perks; AAdvantage others. Will he get more out of Avios? Sure, complimentary lounge access on domestic US flights is nice, but would would upgrades on the (rare) occasions he flies paid economy be better? How frequently will he really be on BA versus AA metal? Maybe the lower tier on AA is actually more beneficial than the top on BA.