I'm leaning toward AT's myself after witnessing Woody take his FZJ80 on BFG AT/KO(1) up this obstacle at Hot Springs.
Those AT tires are fine when it's dry. Not so good when there is any mud. When we went to WR last time there was a 3x locked 80 with us that struggled a little because the tread doesn't void the mud. In fairness the 80 with us didn't have much wheeling experience. So I'm sure that was a factor. After a little coaching and spotting he did really well. I also had some ATs on my Tundra (Nittos) and they basically were slicks in the mud. Did some (not) awesome unintentional low speed drifting at GSMTR a couple years ago. Luckily didn't hit any people or vehicles.
Still, if you plan to do any wheeling I'd go with a hybrid AT/MT like a Duratrac or go full MT if the vehicle doesn't see much street time. For a DD/wheeler I have been massively impressed with the Duratrac. Everyone that I know that has run them loves them. They are a bit noisy on road but that's to be expected with the tread design. Off road they are fantastic.