From a hygiene perspective, disposable paper towels are far superior to hot-air dryers. The friction of the paper towel has a cleansing effect, and the towel actually removes dirt and germs. The hot-air dryer, in contrast, leaves the dirt and germs in place (to the extent not previously removed by soap and water, which is not 100% effective), and many people are impatient and do not complete drying, so the hands are still somewhat wet.
Environmentally, however, it would seem that electric dryers consume fewer resources than paper towels. But I wonder if there may be an underrated environmental advantage to paper towels: Are they a form of carbon sequestration? After all, we’re taking a portion of a tree and putting it in a landfill. That seems like carbon sequestration to me. Offsetting that, however, is the carbon put into the atmosphere when the towel is manufactured and transported. What is the net effect of using a paper towel, from a carbon sequestration point of view?