When using melee basic attacks, most weapons are about the same.
Axe, +2, 1d12
Sword, +3, 1d10 damage
From what I've read, it's generally assumed by the designers that PCs hit about 60% of the time. If we assume that the Waraxe hits on 10 on a d20 (55%), and the Bastard Sword hits on 9...