I would think that most people who continue to travel on AA, as I do, might do so for the following reason:

Being a resident of the U.S, in particular I fly domestically, therefore having status on AA, which also happens to have some of the lower fares, makes sense. If I had say BA Silver status I would not be able to upgrade, get exit rows etc. on AA flights in the US...I would get to use lounges, but still the domestic upgrade is a big issue.

If one was flying soley transatlantic and soley to LHR then building up status on BA or Virgin would make more sense. Another huge issue is the type of fares you are purchasing, if your concerned about building up status or miles...AA is much easier, even with a lesser Biz or First product.

I think AA could be very, very competitive to BA if they have a flat bed in Biz, some upgraded meal service, and an all suite or upgraded (more enclosed suite in First) and open up a Flagship Lounge at JFK and of course continue the MRTC on the 777.