The base is the same, yes.
Alfredus Choice and Mycroft are really autumnal fragrances, much darker and heavier than the spring and indeed summer offerings. A lot of people like the contrasts in both of them, the heavy bases of vetiver and labdanum with the citrus and jasmine/juniper top notes especially. I have not seen any real preference for one over the other, I have seen though a lot of people will either like both of them or neither.
Mycroft was a response to Baker St (Strop Shoppe) and has a lot of US fans who liked the original Strop Shoppe iteration and Alfredus choice was one of the very first AP Reserve fragrances, I will be resting both of them for a couple of years, they may return at some time in the future though