Although in theory any mushroom could be dried, most often it is only the more "expensive" or rare species (such as porcini/ceps or morels) which are dried since this allows them to stored for an indefinite time and much more easily transported.
Saying that, shitake mushrooms are often found dried and are neither rare nor particularly expensive (indeed, unlike many fungus species they can be successfully cultivated).
Dried mushrooms are also much quicker since they are usually already prepared (washed, sliced, etc) and just have to be rehydrated in water for use. (Also the water the mushrooms have rehydrated in makes a great instant mushroom 'stock')
The flavor of dried mushrooms is more concentrated too and so less is needed for a recipe and I also agree with @BenjamínAbarzúaFernández that dried mushrooms tend to be tougher than fresh mushrooms.
Dried mushrooms are actually used as a different ingredient altogether, in fact the River Cafe Cookbook Green writes:
[Porcini mushrooms] are used throughout the year, not as a substitute for the fresh mushroom, but as a separate valid ingredient in recipes