I can throw in my experience as well, I have offroaded 2 different XJ's, both with about the same curb weight (4300~lbs) one had TSL radials in a 32/10.5 the other Mickey MTZ's in a 33/12.5.
Keeping in mind these two tires are wildly different I'll focus on the width aspect.
The TSL's I found were very easy to use in situations that required low to no speed turning even at 10~psi. +1 for narrow tires
They did however not do well in the deep snow. I had to really abuse the truck to make them work or they would just dig straight down and leave me winching. -1 for narrow tires
In the mud, well they are a TSL, they killed it in the mud, didn't really matter the depth, consistency, etc. I put almost 15,000 miles on them and damn near wore them out before I felt I needed a locker. +1 narrow tires.
Fitment, narrower tires just plain fit better in the wheel well, allow stock back spacing on the rims, etc. +1 narrow tires.
The MTZ's I did not get as much snow wheeling with as I would have liked, but they seemed to do really well the little bit I did. +1 wide tires.
Slow to no speed turning, not so much, the larger contact patch really made the power steering struggle at times, requiring me to turn as I moved often. -1 wide tires.
Mud, they did ok, but I felt that the wider foot print didn't afford me a really solid bite on the ground and had to use more throttle than desired to get through stuff. -1 wide tires.
Fitment, well, they are wide, and that means different offset rims/wheel spacers fender flares to cover them for road use, added stress on wheel bearings/ball joints with the tire leveraging them in a different way from stock. -1 wide tires.
So, I guess I could say that while wide tires look cool, in most applications they probably are not needed.