Disclaimer: Not a mechanic, and I love this truck.
This time of year i leave it in Auto. I noticed the benefits when going up slick wet driveways. Also when going up wet ramps in parking garage. Also when my wife is driving I have her leave it in auto mode. Wet parking garage ramps are too slick for 2WD mode (w/no weight in the rear) because traction control lights come on and the truck struggles for a few seconds, so leaving it in Auto is perfect for that situation. Especially since if i had put in 4 Hi the front end would bind as I make the corners in the parking garage prior to going up the next ramp.
In summary 4 Auto is great for wet/greasy/slick conditions or when your wife is driving. I did some tests pulling into fast moving traffic onto and from a wet roadway (left plenty of space) in 2WD, Auto and 4Hi . In 2WD the traction control lights come on as the rears spin and acceleration is poor. In Auto as the rear starts to spin it engages/disengages the clutch packs in the Transfer Case and starts transferring power up into the front wheels (this clutch engagement wasn't noticeable too me, i suspect it happens almost instantly). In 4WD HI my rear tells me the acceleration was the same as in Auto as far as I could perceive. However the front was binding as i was making the slow tight turns on wet pavement.
I "think" I can feel a little more weight in the steering wheel and heavier body motion when its in Auto mode vs 2WD. I notices this when going overspeed humps it "feels" a little different. I asked my wife and she says she couldn't tell the difference. I don't know if i'm detecting phantom motion or its just responding a little differently going over bumps.