The 737 fail operational system is actually more modern than the A320 one, by around 15 years. Still, the operation is in many ways hampered by the insistence on single channel approaches which is neither necessary nor clever.
Ever had the AP disconnect close to DH on an actual CATIII appr? I have. There is a certain startle effect to it and still in the milk, there isn't much visual to go by. It's essential that the crew has the motor skills quick at hand to perform a manual go-around. I again boast that a single channel approach should be standard if the weather is reasonable, as it might be the only real (and I mean real, not simulated) practice you may get at one. One day you might need it.