Sanity check before folks go and gear swap or trade their trucks in.
6 or 7 years ago you would absolutely be correct in that you do not want the numerically lower gear if you had plans for towing heavy. Back then we were running 5 and 6 speed transmissions. These new 8/10 speed transmissions are game changers and significantly bridge the gap between rear end ratios. I would only consider a gear swap on these new Rams if I was swapping to huge tires, pulling out stumps, or just had to have the faster off the line acceleration.
For towing, unless you're the rare Ram owner who has an option light (high payload) model and tow solo with nothing in the truck, you'll never reach the 3.92 max tow rating before overloading. If you're towing realistic half ton pickup trailer loads of 5-8k, I highly recommend you try out the 3.21's before you swap.
There are not a lot of towing reports on the 3.21 to reference. Take a look at this F150 V8 5.0 (very similar HP/Torque/Power curves to the Hemi 5.7).
The Ford has 3.55 gears w/ the 6 speed and killed it on a very difficult towing test in the Rockies towing 9000 lbs. Now compare the gear by gear mechanical advantage of the Ford 6R80 w/3.55 to the Ram ZF8 w/3.21.
---- Ford Ram
1st 14.80 15.09
2nd 8.31 10.05
3rd 5.40 6.74
4th 4.05 5.36
5th 3.05 4.14
6th 2.45 3.21
The Ram with the 3.21's is putting more power (and engine braking downhill) to the wheels than this F150 in every gear. My point is the Ram 1500 with 3.21's offers improved towing performance compared to this F150 w/3.55's (a great towing truck - and truth be told it also outperforms vs Ford 3.73's).
If that performance by the Ford was just too slow up the mountain for you by all means swap your gears out (but go to 4.10's if you're going to the trouble).