I've been through 3 different sets of mud terrains at 3 different tire sizes. I started with 31x10.50x15's on first generation BFG KM's. Wore them out and bumped to 32x11.50.15's on Cooper's first gen STT's. The Coopers were tough as nails with their Armor Tek3 sidewall construction,
https://www.coopertires.com.au/coop...oopers-proven-armor-tek3-carcass-construction
They were loud as heck though, and were hard to keep balanced. Didn't wear well either. Barely got 30k out of them. From what I've read so far about the 2nd. generation STT Pro, they have made some improvements. It's still a mud terrain, is noisy, and has a tendency to cup as they wear if you are not religious on frequent rotations.
My 3rd set bumped me to 33x10.50x15 BFG KM2's. Once again, a mud terrain. Initially, they were relatively quiet for a M/T, but as they wore, they became irritatingly loud. (as a side note, I ran all these tires at 26-27psi., and rotated every 5000 miles. All choices were load C.)
The KM2's wore fairly well, but I couldn't take the noise anymore, so at 6/32's tread depth left, I decided to try an All Terrain.
My 4th. and current set is 33x10.50x15 BFG KO2's. I've got 7k miles on them so far, and by far are my favorite tire to date. I daily my TJ, and this tire really shines on pavement, in pouring rain, and most recently, found them perform quite well in snow. Sloppy mud, they suck.
In summary, stick with a 15x8 wheel, a load range "C" tire, and run them at 26-28psi. My personal preference is the narrower 10.50 section width. They just plain handle better in most conditions, except maybe sand. I haven't tried that media with them yet.