Thanks to all the replies about cat III. l just recall, years ago, going into ATL on Delta when it was very foggy, and the captain bragging to the passengers about how we were going to land when a lot of others were not, because we had a fancy new plane with a fancy new autopilot. Maybe it was cat IIIb or c?
I've hand flown both a -7 and my own -10 on instruments; the -10 is definitely more stable. I'm in the "you must be able to hand fly in IMC; but an autopilot is a great fatigue relief" camp. Some time ago I was right seat to an instrument student in a -10. I had him hand-fly the first two legs of the cross-country, including an ILS in actual with a ceiling at 230'. He did a good job. On the last leg, home, I let him use the autopilot. After just 5 minutes, he said, "I can't believe how much easier this is!". OTOH, on his instrument check ride, everything went well until they returned home. The DPE almost forgot, but then remembered, that he was supposed to check him on autopilot use, so at the last minute he asked to see a coupled approach. Somehow a wrong button was pushed, and the candidate didn't detect it in time, and flew thru the final approach course. The next day he and I did the same approach, and everything worked. So he clearly had pushed a wrong button at some point. Flew again with the DPE and all was well. The point being, these autopilots are great, but you do have to do some studying and really understand how they work. They'll only do what you tell them to do.