I'm not sure how the quarter inching valve actually works as I have not tried one. From Art's description, I take it that the 3PH will either move in fixed small steps, or through its entire range, depending on how much you push the control lever.
Position control for me has only been an advantage with my brush hog. Generally it is desirable to have the front a little lower than the back. [granted there may be times to have the front higher than the back, if you want to grind things up well].
On a flat surface I can set the height of the front of the rotary cutter with respect to the back, by positioning the 3PH arms where I need to. Then I set the stop on the fender slot, so the lever cannot be moved further in the lower direction.
After doing this, I can lift the cutter for transport and when I lower it I KNOW the front is where it I want it. If I need to raise it for whatever reason...when I lower it again, it is right back where it should be.
I guess chains hooked to the front of the cutter and somewhere on the back of the tractor are used for the same purpose...
Other than this one use, I think the quarter-inching valve would work as well for me as the position control does...