AT boots are much lighter than alpine boots, so that's a big advantage. They also have a full vibram-like sole, so you can move around on the ice and hike in them. Try doing that with alpine boots. They also take crampons fairly easily, even the wire bale style.
Most AT boots tend to not have the forward lean and stiff plastics that a lot of alpine boots have. Some people complain they wind up "in the back seat" easily. In general, they won't ski as well as alpine boots, as they are trying to be somewhat dual purpose. I couldn't imagine lugging alpine boots up something like Baker or Hood though, and I only own AT boots, no alpine boots.