Swords are generally more lighter than axes thus they used more as a slashing and lacerations which inflicts mild amounts of bleeding but nothing specific, however an axe is kind of like a hammer and a blade, its heavy, a slow swing, and when it hits the blade cuts into the target, pushes in and causes immense bleeding and trauma.
And that axe being heavy, you'd think the strike would cause periodic critical hits (lucky shot with the blow that hits far harder, doing more damage)
I don't see a light sword doing critical hits as it doesn't hit hard enough, but that's just me.