I do have no personal experience with the Anakee II. Personally I am only familiar with version I.
From the German GS-ers comments I can't see any relevant mileage advantage of the version II over I. The wet grip is further improved, and general grip as well (breaking, cornering etc). High speed stability is not as what some others tires have to offer.
Looking for a good touring tire I would not be put off by the results and ranking as given here:
Choosing the right tire. As a mileage tire it might not be the very best choice.