Are mercury vapor light bulbs which cycle on and off through out the night energy efficient vs fluorescent flood lights mounted on a motion detecting fixture?

First, if your Mercury vapor lights are cycling on and off you probably have a bad ballast. Any ballasted bulb will be much less efficient when cycling on and off. The greatest amount of power is used when the power is first transmitted through the gas within the bulb. Second, Florescent bulbs are just about as efficient as mercury vapor lumen for lumen. Hope this helps Terry