I have only anecdotal evidence but I believe more energy is used to heat the water than the clay saucer. I say that because my vents are closed a lot more with the saucer than with water to hold the same cooker temp.
I have used both and I like the saucer better it heats up faster with a very even heat ,i have never checked but would guess it to use less coal to do the job less mass to heat .
Yup on the phase change (liquid to steam). It requires more energy when you replenish the water during long smokes too. I converted from water to a foil wrapped clay saucer after 5 smokes. My reason was not energy use but cleanup. Dealing with a quart+ of grease water is problematic. You should not dump it down the drain nor pitch in the yard. The latter will attract vermin and rodents. You could dump it in a trash bag full of old newspaper. The foil wrapped clay saucer in a top wrapped water bowl to catch the drippings is a consistent heat sink that is easier to clean.