Ronny Dahl recently put out a great video on this topic that does a good job laying out the pros and cons for both types of tire:
About the only thing he really doesn't talk about is performance on wet pavement, where A/T's undoubtedly have the edge.
My conclusion was that the correct answer for you really depends on how and where you use your rig. If you spend a very large amount of time off road, MT's, while if you spend a good deal of time on road or use your rig for other stuff besides adventures, AT's all the way. For me, living in central Alberta, it's absolutely A/T's since my truck has to go a long way on the highway to get to anywhere to go wheeling/overlanding, and I use it as a homestead truck much of the time, not just an adventure rig.
I run Motomaster A/T's, but they're apparently rebranded Cooper Discoverer A/T's, which are very good.