They do, but how often do you use the axes 360 swing? The 3 hex cleave and 2 hex swing from the greatsword seem to outweigh the axe’s increased damage.
If I want to destroy a shield, I’ll use a 1 handed axe from another warrior, to set up the dude with the giant 2 hander. Wasting a 2 handed attack to break a shield is sorta meh.
Your mileage may vary, but that’s just what I’ve found suits my style.