I bought 33X10" tires for my WK because I want to keep all the turning radius I can, and I believe they are better in the terrain I run. Haven't gotten the lift on yet, so can't give a personal assessment, but I did study the question of width for many hours, and I'm an engineer so I'm pretty good at sorting out reasons that matter to me from personal preference of an author, or an application they have but I don't.
Many people buy their tires for looks, and wide tires look tougher than narrow tires to most people. I'm not immune to how my vehicle looks, but I also think 10" wide mud tread looks pretty tough. You also have very few options for narrow tires, unless your rim size is 15". My WK needs 17" rims minimum to clear the brakes, so I found only a few options that were 10.5" or less.
Looking at articles where a scientific approach was taken, narrower tires almost always do better off-road, and where they don't it's a negligible difference. For things like jeeps, on road you will notice they don't wander in the ruts as bad (I have seen this personally on several rigs), they don't bump steer as bad, and they don't pull in the water puddles as bad. Many people intuitively think you get a bigger footprint with a wider tire, but that is not true at the same psi.
When you air down, your footprint area is exactly the weight on each tire divided by the psi you select (this was a test question on an engineering exam). With a wide tire, it will be a wider pattern but the same area. With a narrow tire, it will be a longer pattern with the same area. For sand, there is a theory that a wide pattern keeps you on top when you're already moving, but I don't buy it. I think the sand comes down to how many pounds per square inch you expect it to hold up. With really deep mud that you're going to try to fly across at high speed and stay floating, I do buy the theory that the wider front pattern keeps you up on top. I don't know anybody, other than during a competition, that flies into mudholes so fast they will skip across.
For rocks, logs, and tree roots, narrow is better (at the same psi) because it will wrap over the edge that you're trying to get over and pull you over it (think of a log sideways, or a big rock step up). A wide tire in that instance will create a wide grip of this edge, and be less inclined to step over it.
For turning radius, tire clearance, and part wear, narrow is absolutely better. I've excluded the discussion of high speed pavement use, because this forum is offroad, but wider is better for high speed pavement where you're sliding around corners and cooking your tires. So, put wide tires on your corvette or crotch rocket, and narrow ones on your trail rig, in my opinion.
And don't believe your tire store when they tell you they don't exist. Those guys have a limited catalog from each manufacturer, and when they told me nobody made a 33X10.5, I found several on the internet, including the 33.3"X10" tires, then I told those guys exactly what to order. They ordered tires their computer said didn't exist.