In the current JAGS rules Axe is just plain "worse" than sword (for one version of Axe and Sword). Here's the current thinking:
Sword: 6 PEN, Med Reach, 1 hand, 5 REA to swing, 5 REA Back Swing, two attacks per round at L3
Axe: 8 PEN, Med Reach, 2 hands, 5 REA to swing, 7 REA Back swing, -1 to block, two attacks per round at L3
The numbers, for the 8 AP Herds balance.