Really? It is not rare, you just weren't looking :o) Sure, such event calls for clear sky but that's about it. Moon needs to be either approaching full-moon phase or a bit after that ("gibbous moon") - there is enough light reflected from the moon and in the same time moon and sun are at a proper angle so they can be both seen at the opposite sides of the sky.
As for the choice - sun is obviously more important but without moon we would be screwed as well (or maybe not? maybe if we didn't have moon in the first place nature would be prepared for lack of tides and unstable earth's axis).