Time for a serious answer
Twohanded axes:
- Better animations (addition length, less glancing, more early on in swings damage, easier to aim for headcuts)
- Unbalanced (trait, not unbalanced as in OP or UP). This means that they are harder (almost impossible) to feint with, they slow you down more and they are also generally slower than their polearms counter part.
Polearms axes:
- Can rear horses.
- Most of them are balanced (not unbalanced).
- Some (primarily poleaxes) are longer.
The only reason you would pick a twohanded axe over any of the other two handed weapons (that are top tier. E.g. Great Swords) would be to destroy shields or for looks. I would not recommend anyone new to the game to use an unbalanced weapon as it is bad in so many ways.
On the other hand poleaxes and the great long axe are good weapons, that in most cases perform better than twohanded axes.