I went through this last spring. I was deciding between the KO2 and the AT3. I read many reviews and watched a lot of videos on YouTube. In the end here is what I found.
Daily Driving - The KO2 were given better rating than the AT3 for on road performance. Tires are quite, very controllable, handles corners well and feels more like a road tire than a off-road tire.
Rain - Both tires seem to preform equally in this area.
Snow - The AT3 on average was given slightly better review in snow compared to the KO2.
Mud and Dirt - Both tires seem to be fairly equal.
Rock - KO2 on average we’re given slightly better reviews in this area.
Overall I think both tires are fairly equal in performance and you can’t go wrong with either one. For on-road performance the KO2 is the clear leader in the All Terrain Tires. They are quiet and handle very well. For snow some reviews thought the KO2 were better and others thought the AT3 were better but more reviews favored the AT3. For rock the same thing but more favored the KO2. Cost wise the AT3 is generally less expensive that the KO2.
For me I bought the KO2. I’ve had them on my SUVs for the last 20 years and they have always been a great tire. I live in Northern California and most of my driving is on the road but I do occasionally go off-road and drive in the snow in the Sierra mountain. So it’s perfect for my needs. Over the years I only had a problem once in the snow. I had trouble stopping my car because I hit a patch of ice when I was in the town of Truckee. Fortunately I was able to avoid hitting anyone.
I hope this helps you out.
Here is a good review but this one says the KO2 is better in the snow.
Falken Wildpeak AT3W vs BFG KO2 - Which Should You Choose?