!!! On both B737 and A320, autoland is a captain's (LHS) landing. At 100' above decision, captain looks out, f/o continues to monitor. Captain makes decision and calls it. Hopefully remembers to take out autopilot before taxying.
For Cat IIIB, there are no calls after "Land Green" at 400' RA. You go around for the big red flashing light. Otherwise you land! Coool!
On the airbus, you have to pull back the thrust levers to land. With autothrottle on the B737, you don't. So in terms of autolands, the B737 is more automatic than the airbus. But then it doesn't have IIIB.