both are great tires.
AT3W just got updated to AT4W, so if you decide to go with Falkens, go with AT4W so when you need to swap 1 for whatever reasons, you don't need to buy a new set.
There is also KO3, but they are not available on the market yet. Only found on select OE trucks like Ranger Raptor.
As a guy who does mounting and balancing as part of his job, I like AT3W because they are always easier to balance. So that's why I went with AT3W.
I have AT3W on my previous rig and put about 10k miles of abuse on them in all kinds of scenarios short of towing (pavement, off pavement, gravel, crawling, high speed desert run, snow offroading) and it was great. Not once did I feel like I was losing traction. 10k miles of abuse later the treads still look like new lol
So I went with AT3W again on this truck and put down 10k miles of abuse already (short of towing and snow). So far so good.