My experience BA-AA was a bit of a nightmare.
BA1477 arrives 1030 to jump AA729 at 1205.
Ended up in a massive queue, to then wait to get our flight called to join another queue, to then wait and get called to just head straight to the gate and get our passport checked there. Made it, and it seems a lot of people are in the same boat so they are prepared to handle the rush, but it is a rush.