There are a lot of factors that should be considered. The moon phase is just 1 of many! A lot depends on the time of year and conditions of the particular hunt. If you are hunting archery high alpine bucks in Wyo or Colo with a full moon with 70 to 80 degree daytime temps I would venture a guess that buck activity would mostly be limited to early/late in the day and night. Obviously they may get up mid-day to stretch and feed but for the most part they are going to lay in a cool, breezy, shaded spot during daylight.
If you are hunting late season in November in Colo with deep snow and clouds all night with a full moon in a unit with little hunting pressure the bucks may be active all day. If you are in a different unit in Colo with lots of OTC elk hunters (lots of hunting pressure) and the same weather/moon phase the bucks may not be active much until dark. I've hunted one of the premier muley units in Colo during the 4th season with 60 degree days, full moon, little hunting pressure in a year with little snow....and it was a super tough hunt. The bucks hadn't migrated into the unit due to lack of snow and were spooked into thick trees patches up high by all the OTC elk hunters. It was a super tough hunt! Even the next year with 0 moon with the same warm temps and 0 snow it would also be super tough hunt!
With that said, there are a lot of conditions (moon phase, depth of snow, daytime temps, browse and water, hunting pressure, migration, rut activity, velvet vs shedding velvet timing, etc) that all should be considered when picking units, hunt timing, particular year to draw a tag, etc).
