Warriors appear to be better armed and typically show up with a onehander+axe. The axemen appear to have a random chance of spawning with a war axe and throwing axes. They both have about the same armor. Axemen can upgrade into berserkers, so that's the only reason I would take them over warriors.
Upgrading to Axemen is a mistake (only if your team's Training capability sucks and you need some stronger troops right now it can be considered as a right thing to do). Warriors have throwing weapons - welcoming addition to green horde. Warriors can be upgraded to Armored Axemen (or Berserkers) very fast. Armored Axemen are very strong troops, almost Huscarls, much better than simple Axemen with the same field role.
It depends on your point of view - the axers are more heavily armoured than the warriors, have better stats and skills (thus higher level) and their short axes make them deadly in close combat. And that´s where I use them mostly up the ladder gogogogo!