Just to flip it on its head, here is one real world test:
http://news.pickuptrucks.com/2016/03/winter-tire-test-some-treads-are-better-than-others.html
Hint: The AS out accelerated the top rated AT tire, but performed worse in the braking test and was outperformed on the track.
You may have it in your head that an All Terrain tire has to be harder and therefore can't perform better than an AS. Reality is not that simple.
http://news.pickuptrucks.com/2016/03/winter-tire-test-some-treads-are-better-than-others.html
Hint: The AS out accelerated the top rated AT tire, but performed worse in the braking test and was outperformed on the track.
You may have it in your head that an All Terrain tire has to be harder and therefore can't perform better than an AS. Reality is not that simple.