The Hankooks are great. I really liked them. More road noise than I expected, but not bad at all. Great in most conditions I encounter (rain, snow, heat, cold, gravel roads, etc.) I liked that they had a rim protection flange. I also liked the solid white lettering. They looked good and worked great.
The Falkens suck. They picked up rocks worse than any tire I've ever used. Then those rocks get thrown all over your rocker panels when you hit the pavement again. They also had miserable traction in wet offroad conditions. When new, the rubber compound literally gave off an odor similar to cow feces. They also had a tendency to track all over the lane and felt "squirrely" until they wore down some. And finally, they are VERY HEAVY and my gas mileage took a nose dive with them. They did have thick sidewalls which would be a plus for guys who live around rocky environments. But I personally will never run them again. They are made by Sumitomo, and there is a reason why the Sumitomo AT was discontinued.
The Goodyear Duratracs were great. Very quiet for the first 5,000 miles. Then I cross-rotated them for the first time and they got noticeably louder. They still were not quite as loud as a full MT tire. I enjoyed them a lot. On wet pavement they did not excel. However, in mud and deep snow they were excellent. The sidewalls were weak and the price is ridiculous for what you get. However, overall they were good tires and I would run them again if they weren't priced so high.
There are dozens of other good choices I've run on my 4x4s but the Cooper AT3 is currently the reigning champion and I will run those forevermore unless somebody releases a tire that works better in all conditions, which hasn't happened yet.