"U" is the correct class, and (at least in Sabre) it does map into business class (not economy plus or whatever other confusing name they're calling their "W" class).

Looks like you were a victim of BA's surly class-system arrogance. Since the ticket was issued by AA, I would demand compensation (at least the difference between full J and full W on the route) from AA; they in turn can get money back from BA. Today that's $439.90 ($2980.10 vs $3360.00).

And yes, you would have been better on CX. Check out this thread: http://www.flyertalk.com/forum/Forum85/HTML/000427.html