Actually, my experience with BA has been quite the opposite. Literally every time I have flown with them there has been a serious screw up. Usually they have reassigned my seats to the worst possible seats on the plane despite my having decent seat assignments in the first place. This has even happened after checking in, getting seat assignment and then being reassigned at the gate. They certainly do muddle and then, in my experience, slap you around because they are confused. On the other hand I have never had anything even approaching difficulty with CX despite having always booked through AA. Guess it all depends on the luck of the draw.