I've had a few of these tires so can share experience. (2 sets of the falkens) (1 set of AT3's). Every one of the options you've picked are great tires so this is more of subjective notes. We put about 10k total miles on our cruiser a year. It breaks down this way: about 100 miles in 4LO, 500 miles of low maintenance roads, 1k of gravel driving, 500 miles of towing, and 50/50 - town/highway for the rest.
Falkens: Have 50k miles of experience on these (on second set) with my LC.
Pros: Have worn well. Quiet on road. Handle well in turns, wet roads, gravel, etc. I like that they don't collect hundreds of small rocks like other AT's I've had - throwing off high speed balance. Sidewalls are very tough, they handle being aired down (low) very well. They just do not "chunk" like BFG's I've had before, and personally I think they look great.
Cons: Man these are heavy - so are all LT's. Each time I've bought 5 tires, and one just wouldn't balance right. Discount is always cool and swapped them, issue gone. LT's ride a lot rougher than P rated, noticeably rougher than C. I'd consider that.
Coopers: I have 30k of experience with these on my 1st Gen Tundra. Man are these good tires, and at such a great price.
Pros: Have worn awesome. On road performance is fantastic - very quiet, soak up imperfections, handle adverse road conditions, shockingly good in the snow. I think its the case of them being load C's. They balanced very easily and never had any vibrations or anything weird. These things do very well off-road when you air them down. Seems like there are usually a $50-70 visa card rebate going.
Cons: they don't look as aggressive, but I don't care. I wouldn't air them down as much as an LT just to keep the sidewall from folding. They pick up very small pebbles more easily than larger lug tires, but I never noticed balancing issues because of it.
Toyo Open Country AT2's: The guys that work on the drilling rigs all over Colorado seem to run these on the 3/4 and 1 ton trucks almost exclusively. Have heard from a lot of folks that they are super durable tires and wear like iron on the heavier trucks.
If I didn't have a fresh set of the Falken's on the LC now (they looked good in the store and the Cooper's were just a little more money) I'd put the Coopers on this thing instead. They are that good.