To actually know which is better we shouldn't be making armoured legendary pickdwarfs and axedwarfs beat each other.
I think we should try to simulate an actual ambush or early siege - 8-12 goblins in leather clothing with half copper/half iron shirt/breasplate, helmet and shield, all competent or skilled in weapon skills.
Then we make them fight either "early military" or "emergency miner squad"
"early military" is 6-8 (all 10 soldiers aren't going to be all awake and close and not stupid enough to be in place in time) dwarves in full iron armour wielding iron, maybe steel axe or two, and shields, adequate to skilled in combat skills.
"emergency miner squad" is 6-8 Talented to Master miners with assorted picks - 2 copper, some iron, bronze and steel and without shields or armor. (This can be simulated by modding pick to use AXE skill).
I'll update the post as i would have conducted the experiments
update:
i've done some arena testing
early military was 6 dwarver in iron helm, mail shirt, greaves, gauntlets, high boots, with a wooden shield and an iron axe. All combat skiills compenent
miner squad was 6 dwarves with bronze axepicks (picks modded to use AXE skill)dressed in leather clothing, with Professional axedwarf and no other skills.
goblin ambush was represented by 8 goblins competent in combat skills, dressed in leather clothing, iron mail shirt, iron shield, iron helm and iron weapon.
10 gob squads with differrent weapons had to fight early military and miner squad.
The simulation is meant to somewhat model a second spring or summer ambush.
the negative/positive number indicates survived uninjured or lightly injured dwarves/goblins, the number with "i" multuplier means severely injured ones (severed limbs and\or unable to stand)
The top string is selected weapon of goblin ambushers.
warhammer mace flail s. sword halberd b.axe spear whip pike l. sword maul mstar scourge g.axe
em 5+2i 6+2i -2-3i 5+3i -6 3+2i 3+3i 3+4i -5-i
ms -4-i -2 -3-i -4-i -5 -4 -6 -4 -4 -6
According to this simulation, pick in hands of well-trained miner (you are going to have them anyway) is much better at fighting goblins then any military you can have early in the most of games - miners never lost a single match, and the axedwarves were only able to defeat goblins with large unwieldy weapons.