Both mustaches and beards have their perks. Mustaches can be twirled in a scheming manner and beards can be stroked in a thoughtful manner. But... to be honest, I've always wanted a long grey beard to stroke and twirl as I think deeply about the intrinsic and metaphysical questions of the world. Like this one. :]
I think both are pretty awesome, if you can pull it off. Personally, If I could grow one, I would say a mustache.
As previously stated, it is there for twirling into whimsical shapes. My dad always had quite the flair when twirling his. Much like Eleanor I like the handlebar quite a bit, as well as the sparrow, Klingon, and the Zappa.