This was an interesting thread, so I decided to do a couple tests my self.
Using sword - weapon dmg range was 109 - 1092, average of 660.5. Actual average was 600.5, so a 11% increase over the weapon damage (would imply a 11% crit chance assuming crit is dbl dmg).
Using axe - weapon dmg range was 392 - 471, average of 431.5. Actual average was 575, so a 33% increase over the weapon damage (would imply a 33% crit chance assuming crit is dbl dmg).
My weapons were different ee, so going back to Light_prince's dmg calcs and assuming sword has a crit chance of 11%, axe 33%
555 * 1.33 = 738
664 * 1.11 = 737
So the average actual damage for axes/swords is the "same", I feel like the game was designed where it doesn't matter which weapon u use, the damage is the same when factoring in crit, so there is no weapon advantage when basing it on damage.
Now, there is an advantage as others have mentioned where swords will over hit a lot more, making their true damage less as a lot was used to overkill monsters. As you get to higher levels this is less relevant as it takes 4+ hits to kill a mob.
Obviously gear/prof/how a char is stated/skills etc will change which is better, but I would say generally the more consistent dmg is better (just like why ices are generally better than the other charms). That being said, I still use and love my swords