In my experience, BA is incredibly conservative and far more proactive in offloading passengers, at least in comparison to the US legacy carriers. While AA really won't start offloading you until you're clearly not there and it's time to get standby passengers on the plane and then depart, BA will basically automatically move you if the computer says you cannot make the connection. BA will almost never hold a plane for a large number of passengers, because Heathrow is so slot constrained, whereas a US-based carrier will typically hold a plane if that many people are going to be a few minutes late.
I'm not really sure why the approaches seem so different, though I know I prefer the approach that attempts to get as many people there on-time as possible.
