Anyone can use it, but only a warrior or warrior subclass will have the axe skills for it. And the Chaos axe is just as good as any other axe. You can get one with max damage or you can get one that's less. You can get one with mods (shelter, sundering, etc) or you can add your own mods later.
Axes attack the same speed as swords, however they have a wider damage range. Swords at maximum do 15-22, whereas axes do 6-28. IMO it's a fair trade-off because there alot of damage-dealing axe skills (more sword attacks deal conditions) so in theory you can use an attack skill every second attack.
Warriors can wield swords, hammers and axes.