Longtime Engineer by trade. 1st time poster and short time smoker. Currently learning the in's and out's of a $299 Masterbuilt Stainless Steel Electric smoker from Sam's club. This smoker has a temperature controller that makes it very easy to maintain a temperature (provided you are not peeking).
In an Electric smoker, a pan of water may be a requirement. I know that electric ovens are dryer than gas ovens. Wood fuel (and charcoal) would also have a certain amount of water within it which may help to account for the overall preference of charcoal etc. I can say from an Engineering perspective that a pan of water would assist with temperature control of any fire based smoker.
We all know from our science classes that water boils at 212F (sea level). What we may not remember, is that it takes a significant amount of energy (heat) to convert the water into steam. A large pan of water would definately help to keep the temperature within an oven stable at slightly higher than 212F. If the oven temperature were exactly 212 the energy (heat) would be absorbed by the water rather slowly. The extra heat we see for a typical recipe (225F) provides enough energy to covert the water to steam. In this case the water provides a large heat sink of sorts, helping to maintain the oven temperature.
This effect is very much the same as the ~150F plateu we see with meats as the fat and connective tissue is being rendered into liquid. This rendering takes energy, and results directly in the temperature slowdown we have all seen. A glass of Ice water is very simlar in this respect. The temperature of the water will remain almost exactly at 32F until all of the ice has melted (rendered). This is what makes a full glass of ice & water ideal for calibrating cold thermometers. The same would be true for a boiling pot of water. If the thermometer is held off of the container walls, you can be very sure that the temperature of the water would be very close to boiling.
With all of this being said, hopefully you can see how the water is very good at helping to keep temperature under control.
A fire based smoker without a pan of water would be much more sensitive with respect to keeping the temperatures steady. I could probably say that it requires much more fiddling by the operator to keep a wood fired smoker's temperature steady.
I cannot say one way or another if the extra water vapor helps to keep the meat moist or not. It would certainly seem to be the case although I have not tried to run my smoker dry yet. It may also help the smoke attach itself or be absorbed into the meat (definitely not a chemist here).
Hopefully this will help someone, one way or another.