I'm curious about why you went from 12.50 mud terrains to more narrow all terrains?
A few reasons. One is that I used to have a '75 CJ5. As I was rebuilding the Bronco I needed tires for the CJ, so I put the Mud Terrains on it. When I sold the CJ I had the two sets of wheels, and only the ones with the Mud Terrains fit the Jeep while both sets fit the Bronco, so I sold the M/Ts with the Jeep.
Also I daily drive the Bronco and the narrower A/Ts handle better. So they are a clear winner there.
I do 'wheel it (rocks mostly). For trail use I have mixed feelings between the wider and narrower tires. The CJ was my first trail rig. It started with 235/85-16 BFG M/Ts. When they wore out I went to the 33/12.50s, and now I've 'wheeled the Bronco on 33/9.50 A/Ts and the 33/10.50s on it now. The 235/85-16 were load range E so those were too stiff, rode rough and didn't give great traction (wouldn't conform as well). But all of the others have been pretty good for me in the rocks or in general trail riding.
The wide tires MAYBE rode a little better aired down, but the difference wasn't huge, and I also am comparing two different vehicles. The narrow ones seem a little easier to pick a line with, not catching on rocks or trees as often. But then again, it's easier to keep the wide tires on top of the high points and I never hit a hub on the rocks when it was buried inside a wide tire. The narrow tires do have a HUGE advantage when it's time to air back up. Probably half the time to fill the smaller volume.
As far as the tread goes, the M/Ts definitely had an edge in mud, but I try to avoid that (I did get the Bronco stuck once where M/Ts might have let me back out). On rocks I'm not sure that there's much difference. The lugs on the M/Ts grab edges of rocks well, but the A/Ts seem to grip smoother rock surfaces better. And the narrow A/Ts work a lot better in the snow I've driven in (about axle deep), although I could see wide M/Ts working well in deep stuff.