Hi
britflyer
I'm no expert on this (and am prepared to be corrected!) but seeing as no-one else has answered you yet, my understanding is that *A carriers are unlikely to match *A status as part of the whole working together thing includes not pinching each other's frequent flyers! UA are *A too, so the same would probably apply.
BA, being One World, would be likely to match your status. However, I very much doubt your customer service experience would improve...