I think there is a point that the whole Nautilus line is too tame as a sports watch line up.
Then again, so is the AP, except for some of the limited editions such as the Barricello (the original one).
Personally, the most sports-like watch to me are the Rolexes, and they are very rugged, too. I have no idea how fragile a Nautilus or AP may be, but somehow these are not watches I will wear when I go scuba diving. Humm, perhaps this is a test (not "the" test, just a test for some of us): a sports watch is something you'd play the roughest sport with, assuming you will wear a watch doing sports, not something that looks sporty.
As a sporty looking watch, however, I think 5711 is better than AP, because AP are too thick. I choose 5711 because it is clean. 5712 has always looked to me to be a little strange: moon phase and power reserve don't go with the notion of a sports watch (for a start, a sporty person will sooner be dead than have a watch which has no power because of a lack of wrist movement...).
But you can probably discount everything that I said since I do not have a 5711 but have a 5712 and a couple of APs (and more sports Rolex than I need)...