The monitored approach comes in many different versions. However, all have the same essential element in that one pilot flies the aircraft (with the automatics) and the other monitors both the flight path and the outside view, especially approaching DA/DH. It was originally developed by BA ans has since been copied by companies worldwide in various guises.
Whether this involves the FO flying the a/c and the Captain doing the landing (usually an autoland but not necessarily so) or vice versa, doesn't much matter. It's simply THE outstanding manner in which to conduct an approach to minimums regardless of whether it's CAT 1 or Cat 111 or even a Non-Precision Approach. Inh fact I would venture to suggest that the NPA to minimums is the one where it's probably most needed.
Lots of pilots have rubbished this method over the years without trying it out to see just how well it works and how much it adds to safety near the ground when the weather is lousy. Sure, some companies have gone overborad and made it unnecessarily complicated but that doesn't negate the value. However, as stated earlier by another poster, it does require good training and, most of all, good flight deck discipline. I just wish we had it in my current outfit.