I've had all three, with the Coopers on my truck right now. Mine are 285 75 16, since I have an 80 with stock wheels (until next week...)
Coopers - have been great. Wearing super well, have fantastic traction on road dry or wet, and better traction off road in the loose stuff (mud, snow, deep sand) than the Falkens, about equal in regular off road usage. I've got 35,000 miles on them right now and they are just beginning to show noticeable wear.
Falken - Had these for four years and 44,000 miles, and I wouldn't have gone away from them if I could have gotten them. They were simply unavailable in my size when I needed new tires. I was told by the rep that "No one is making 16" tires anymore, so you'll see this more often." meh, whatever. You can get them all day right now. My only functional complaint with these (as I referenced above) is the loose stuff. I think the new Wildpeaks have a different tread design than mine had, but in sand, mud or snow they were prone to loose spinning. They were GREAT tires all around. Again, only availability made me go to the Coopers.
These pics who two that were warrantied shortly before I went to the Coopers. As I said, there were no WildPeaks to be found at the time, so I used these on my trailer.
BFG AT KO2 - 39,000 miles, the best road manners of all, quiet, great wet and dry traction on the road. Zero complaints off-road never cut a sidewall or had tread blocks break or any of the other BS. When I go to new wheels here next month, I will be going back to these in a 315/17 size. They are significantly lighter than both the Falken or Cooper offerings. Again, I owned all three at the same size, same wheels, that isn't speculation. I weighed them. So why did I change them? We were heading to SPI National Seashore in two days and a vandal slashed my two front tires, while leaving me a note about "gas guzzling SUVs". Yep. Discount only had the Falkens in stock for fast enough turn around for me to still make my SP time, so I went to Falkens.
Unfortunately, I don't have pictures of the truck with the BFGs, but you've all seen them.