I am like most others that have posted here in that I hunt whenever I get the chance. However, I do believe that deer move better during the day when the moon isn't full. Also, I believe that photoperiodism is one of the primary determining factors of when the rut takes place and I try to schedule my vacation accordingly.
From my experience I like to hunt when there is no moon. So deer cannot graze at night which makes them move during the day.
Actually, we use to go out spotting at night, down in Mississippi, (it was legal back then, don't know if it still is or not) and we would always see a lot more deer on nights where there was no moon or little moon compared to nights where the moon was full. I can not think of one exception to that.