I constantly miss my target with the axe because I think it has the same reach as the sword, but it does not. So, 1-0 sword.
Axes do more damage, though. 1-1.
There are many cool versions of both available in mods, and I prefer the Nord style, which again there are plenty of. Both are also good for the viking type warrior I play. so I'll give both a point for style. 2-2.
Sword gets more criticals with the perk, and axes do bleed damage. I'm not exactly sure what the bleed damage amounts to, but I imagine it's good for hit-and-run against powerful enemies and 2h wielders. I'll give axe a point for that as I'm wearing light armor and need to get out of the way of those big swings. 2-3.
But swords have a faster swing rate. 3-3.
This is pretty much where I'm at, and I can't decide. Help!