My character uses a greataxe and will continue doing so no matter the lesser damage, or any other insults that wizards bestows upon axes, yet again, in yet another edition of D&D. I totally concur with GX Sygma. If they wanted to differentiate the three great weapons, they would be better off doing it via fighting style benefits.
I also don't like the fact that greatswords and maul uses roll 2 damage dice, it makes them more reliably attain their average expected damage, and extra dice rolls slow the game down. The d12 becomes another seldom used dice yet again. In one of the earlier playtest packets dwarves got to upgrade their damage dice a step for axes, 2d6 was a very good insurance against rolling a natural 1 for damage on a d12 weapon.
If anything, axes should do 2d6 instead of swords. The chance of doing the least amount of damage is minimized since the impact is concentrated in one area of the weapon. Swords can graze their target more readily than a solid axe hit can.