Attacking faster is a common misconception of how good a weapon is. Both axe and great axe have a much higher damage output than the sword. As Captain WTF!? mentioned, great axe and axe both have a higher cap (I'm pretty sure they're both A+) than sword (B, I think). Since each skill point in a weapon is worth .9 accuracy and .9 attack, that builds up to a significantly higher accuracy and attack which means you'll be hitting more often and for more damage. Sure, you attack slower, but the bigger numbers more than make up for it.