As far as I can tell, the damage increase given by the "power" number scales up according to your weapon. This was an issue with the shaman before: shaman's Rockbiter weapon buff gave a flat damage increase to each attack, so shamen flocked to daggers and other fast weapons because they'd get the most out of it. Since then Blizzard changed Rockbiter to affect your "power" stat, for the explicit reason of taking speed out of the equation.
The advantages of a fast weapon versus a slow one come down to this: fast weapons get more crits and are better for interrupting spells, while slow weapons (because their damage is front-loaded) are better for dealing with heavy armor and damage-reduction abilities.