My hunting experience is limited but I would take no moon over a full moon anyday.
Here is what I experienced. Full Moon - Couldn't sleep because we heard elk bugle all night and at 4:00AM they would stop. Never could find or hear one during daylight.
No moon - Bugleing during the 1st hour of daylight and were moving around during the day. I'm sure others may have had the exact oposite experience but that has been mine so far.