In a jungle environment, the Moon isn't much of a factor, considering you're beneath a couple canopies of growth. Starlight survey lance systems, both tripod mounted and personal goggles, take care of the dark nicely.

Open terrain, such as is found over much of Afghanistan, would beg for a Moonless night for ground ops (on foot), but a well-trained patrol team could make a nearly invisible passage across Moonlit grassland, though I would prefer a Moonless night. Any natural disturbance is used to the advantage, such as moving near dawn, when trade-breezes from atmospheric convection cause the grass to move, or waiting for an expected storm. The middle of the night isn't always the best time to attack.

The night is best for antagonizing your enemy, keeping as many of the bad-guys up and alert as long as possible (what Ali would call "Rope-a-Dope"). Wear him down for a few nights and keep him chasing geese during the daylight hours. After your target has been up and guarding his area for a few days straight (and you've had a nice, relatively comfortable nap) is a pretty good time to mount your moment of truth.

Dan