I have done a moonlight hike a couple of time on both BA and S. Kaibab and prefer S. Kaibab.. you don't have to creep on past the people camping at Indian Gardens and the light is more on the S. Kaibab.. we have hiked all the way to the river by moonlight and back.. the BA depending on the angle of the moon we didn't see any moonlight until we got down to Indian Gardens.. is so neat to do that ... I don't know about the north rim but would think you don't have much moonlight except a little bit on that trail..
--On the loose to climb a mountain, on the loose where I am free. On the loose to live my life the way I think my life should be...For we only have a moment and a whole world yet to see...I'll be looking for tomorrow on the loose. ---unknown--