From my observation, the autostick (with the 2.4L) seems to work best in situations where you want to accelerate faster than normal from a stopped situation.
When you try to accelerate fast using the normal 'D' mode of the CVT, that's when you get the various moaning sounds, and it doesn't seem like you're accelerating very fast. It's a bit deceptive, because you do get up to speed decently. It just doesn't seem like you are.
However, when you use the autostick startking in '1' and press the accelerator hard, the RPM's zoom right up to the 4-5k range, and stay there as you tap the shifter to the right to move up through the "gear range" that Chrysler has programmed into the CVT. This (in my opinion) translates into getting up to a certain speed considerably faster. Be ready to shift quickly though.... the gear range for each click is fairly short. Be sure to not over-rev your engine.
The tachometer never seems to rev as high in normal 'D' mode when accelerating hard. The autostick method guarantees that the engine stays up in the high rpm / torque range.
Just remember to shift it all the way into the 'D' mode after getting up to your cruising speed, so the automatic gearing feature can take back over again.
I think I read that the lower gears in autostick mode can also help when road conditions are bad, etc. But so far the above scenario is how I've been using my autostick feature. The engine definitely makes better sounds using the autostick approach when accelerating briskly, vs. the automatic 'D' mode.