I've read about this in many places with many different reasons given and experienced it more than once. The reason that works best for me is that as the full moon approaches tides and the amount of light are affected both "usually" in a manner leading to higher activity levels for all creatures affected by one or both of these stimuli. Or in other words fish eat more at these times, but they seem to get full a day or so before the full moon or something, so they don't feed as well on the actual full moon.
Also, when it's a full moon there is so much light that the predators don't have an advantage in eyesight, but they seem to have an advantage 2-3 days off of the full moon.
Another possibility that I've heard is that They get tired from being active 24 hours a day before the full and have to rest.
I personally put the most stock in the first one and the other 2 kind of fall in behind.
I don't know if this clarified anything but I hope you'll try fishing anytime you can and especially +/- 2 days from the full moon.

Tight lines,
Wade