There is zero photosynthetic benefit to moon lighting when properly setup. If the moonlight pattern follows the natural lunar cycle in your geographic then there may be a spawning benefit to having them when it comes to fish or corals that spawn based on the lunar cycles because the lunar intensity will follow the gravitational changes that occur during the lunar cycle. I say may because I am not aware of any scientific studies that have been done on synthetic lunar lighting. That said, some people add blue lights to their tank and run them at night and call them lunar lights and run them every night. In those cases, they would have no benefit whatsoever and may be even counter productive if the lighting is too intense as it could disrupt the natural photosynthesis cycle in corals.