I've owned both several times and used them on all types of terrains. My experience is similar to what you'd find online anywhere.
KM2s: (Mud-terrain tires):
Off-road-ability: In off-road deep snow and mud, they're great, because the large lugs clean themselves easily. Great on loose gravel roads, but beware if after-market wheels have pushed your tires out a little and exposed the lugs past the side steps. If you have your windows open and elbow laying on the window sill, flying rocks can easily hit your arm and cause insane amounts of pain and discomfort. Ask me how I know.
On-road-ability: The lack of siping causes limited traction in light snow and ice on pavement. In other words, they suck in light snow and ice on the road. You're better off sledding to your destination, because that's what your truck's gonna do regardless. Dry and light rain is fine on the road. Noise isn't terrible until you reach 1/2 of the tread life. After about 20,000 miles, it get s really loud. You need to rotate religiously every 3k miles because they tend to cup more than other mud-terrains.
KO/KO2s: (All-terrain tires):
Off-road-ability: Great all-around off-roading tire. Great on loose gravel. Not so great in deep mud or snow, but good on light snow or sand. KO2s are better than KOs in mud, but still can't hold a candle to KM2s.
On-road-ability: Good on-road tire with decent traction in all types of weather patterns. Light snow and ice traction is pretty good. Dry weather and light rain is great and it can even do deep snow on pavement pretty well. Lots more siping and soft compound allows for good cold weather traction.
There's no denying that the KM2s are very sexy tires. IMO, the KM2s are one of the nicest looking tire on the market. However, unless I have an off-road-only vehicle like a modded-out truck or Jeep, I prefer to go with a much more civilized KO2. Still aggressive looking, but much better behaved on the road, especially for a daily driver.
Hope this helps.