The biggest advantage is multiplayer. For example, we were playing a PON game with 16 players at one point. Imagine having to send out 15 emails, then get 15 back.
I like to use Dropbox for the 3 or more player games (such as AJE, TEAW, and PON). The other nice thing is you can keep a lot of turns in folders in Dropbox, and look at past turns.
Remember - The beatings will continue until morale improves.