Attention: TDR Forum Junkies 
I've never liked a BFG tire though I have some friends who swear by them. I haven't run a Toyo AT2 but I ran the original AT and MT in multiple sizes. They are excellent tires with great traction and stability. The MTs I most recently ran were 37" and those were the best tires I've ever had. I grossed 30,000 lbs towing to Alaska and back suffering busted wheels but the tires only needed rebalancing. The biggest problems with Toyos are that they are very expensive and I only got 20,000-30,000 miles per set, nearly bald when I'd finally buy new tires. I would have to rebalance the ATs and MTs every 1,000 miles so they were also very high maintenance.
If the Cooper AT3 were available in my size that is what I would run now. On the farm we've run them on a 3/4 ton Suburban that were perfect for years until we parted with the truck and still have them on a Jeep Scrambler. Their performance is excellent in every way. There likely isn't a better tire for your purposes.
I'm on my second set of Yokohama Geolandar tires and they are like driving on balloons, you would hate them. But they last forever, well over 65,000 miles. They quit making them in my size in 2012 so my next tire will likely be the Cooper STT Maxx. If you read the many excellent reviews about these mud tires and think you need a more aggressive tread that is still very well mannered and long lasting on the street you may want these instead of their tamer all terrain tread.
Pretty sure Nitto is made by Toyo as their lower priced, lower quality offering. Too many reviews kept me away from them. And I think I remember seeing them on some off road rigs while four wheeling in Colorado and being very unimpressed.
You also asked about the Falken AT3w and I've come close to trying them myself. They look like a decent tread but there are so few reviews on them that I have yet to feel confident in forming an opinion on them either way. I used to consider Big O as well. And now Amazon has numerous brands that I've never heard of that are building up decent review logs. For a rig that tows I'd rather stick with a bigger brand. Cooper is a huge tire company and I think you would be very happy with one of their truck tires.
If the Cooper AT3 were available in my size that is what I would run now. On the farm we've run them on a 3/4 ton Suburban that were perfect for years until we parted with the truck and still have them on a Jeep Scrambler. Their performance is excellent in every way. There likely isn't a better tire for your purposes.
I'm on my second set of Yokohama Geolandar tires and they are like driving on balloons, you would hate them. But they last forever, well over 65,000 miles. They quit making them in my size in 2012 so my next tire will likely be the Cooper STT Maxx. If you read the many excellent reviews about these mud tires and think you need a more aggressive tread that is still very well mannered and long lasting on the street you may want these instead of their tamer all terrain tread.
Pretty sure Nitto is made by Toyo as their lower priced, lower quality offering. Too many reviews kept me away from them. And I think I remember seeing them on some off road rigs while four wheeling in Colorado and being very unimpressed.
You also asked about the Falken AT3w and I've come close to trying them myself. They look like a decent tread but there are so few reviews on them that I have yet to feel confident in forming an opinion on them either way. I used to consider Big O as well. And now Amazon has numerous brands that I've never heard of that are building up decent review logs. For a rig that tows I'd rather stick with a bigger brand. Cooper is a huge tire company and I think you would be very happy with one of their truck tires.
