Not true.I know the chopping efficency of a kuk is on par with a axe, even better in somecases.
Due to the several factors, the chopping efficiency of a kuk cannot match that of an axe, provided the axe user has adequate space to obtain a full swing.
1) Due to the longer handle of the axe, the axe will deliver more force (larger arc equals more energy).
2) Due to the method of using an axe (when swing with both arms), the axe will deliver even more force.
As for the axe handle breaking, try one of these...
http://www2.fiskars.com/CA/en/Garden/Product+Detail?contentId=78664
Don't get me wrong, kuks are great and I like them too, but they just can't compete with a full size axe when it comes to chopping.