I tested this in the arena 5 times, and the results were... actually very interesting.
Test 1:
Urist, unskilled unarmored dwarf
Cacame, unskilled unarmored elf
Both have iron battle axes.
Cacame immediately chopped Urist's middle finger off, causing it to spray blood. Cacame then took a whack at Urist's left leg, detaching it and sending it flying away. He then hit Urist in the chest with the flat of the axe, bruising his right lung.
Urist then attacked Cacame, but missed, and was rewarded with a hit to the right upper arm that cleanly severed it. Cacame then hacked at Urist's chest with the battle axe, tearing an artery and tearing the right lung apart. Urist immediately bled to death.
Win: Elves
Test 2:
Same parameters.
Urist took Cacame's left lower leg off almost instantly after missing twice. Cacame then hit Urist in the upper body, tearing the fat, and managed to get a lucky hit on Urist's lower body, cutting him in half.
Win: Elves
Test 3:
Same parameters.
Cacame took off Urist's right lower leg. Urist took off Cacame's left upper leg. Cacame took off Urist's right upper leg. Cacame hit Urist in the left lower leg, tearing the muscle, and twisted the axe around. Urist flailed at Cacame for a bit but didn't manage to get a lucky strike. Cacame hit Urist in the upper body, just like in test 2, shattering a rib and tearing the right lung.
Win: Elves
Test 4:
Cacame charged at Urist, tore apart his heart, and cut him in half at the lower body. He then escaped unharmed.
Win: Elves
Test 5:
Urist removed Cacame's left leg with the first blow. He then tore an artery in the elf's chest with his axe and cut the other leg off. Cacame bled to death extremely quickly.
Win: Dwarves
Elves: 4
Dwarves: 1
As much as we may not want to admit it (I personally fed the elves to great whites after the first four tests), elves seem to have better base stats for melee combat than dwarves.