The cluebook mentions some hints towards this.
*** SPOILERS ***
List of average damages, using optimal swing, in vitality points is below. The "Min" is for a weapon that has been barely drawn back and the "Max" is for a weapon that has been drawn back all the way.
A strength factor is also added to the damage score, approximately equal to your strength statistic divided by 18.
Melee Weapon / Min-Max
Hand Axe / 3-4
Axe / 4-8
Battle Axe / 4-13
Jeweled Axe / 4-11
Dagger / 2-3
Shortsword / 3-4
Longsword / 4-8
Broadsword / 4-11
Jeweled Sword / 4-11
Black Sword / 4-12
Cudgel / 3-4
Light Mace / 4-7
Mace / 5-12
Jeweled Mace / 5-15
Fist / 2-3 (barehand skill factors into this, a skill of 30 gets approximately +7 damage)
Missile weapons - does not vary in relation to drawback time
Sling Stone / 3
Arrow / 4.5
Snowball / 4.5
Bolt / 5.5
Acid / 4.5
Magic Arrow / 4.5
Lightning / 8.5
Fireball / 14.5 (area effect)
Unfortunately I can't find a mention of enchantments and how effective they are. You could probably work it out by casting Study Monster after using an enchanted item and a non-enchanted item. My assumption is that each level (minor, major, great, etc) adds an additional 1 average damage, but have nothing to back that up.
So given all the above, my guess is that the Hand Axe of Major Damage would have better minimum damage (5) while the Axe would have better maximum damage (8). Axe still wins in the average damage department I think.