Why is being a hybrid a curse?

From Vampire Diaries Wiki:

Hybrids are obligated to serve Klaus because his blood created them and they feel loyal to him because he freed them from the pain of turning every full moon. They have limited free will, along with lack of control.

This lack of control and their susceptibility to mind-control is a curse which only hybrids have.

EDIT: In light of OP's edit, narrowing down the discussion to Klaus only, the possible explanation is the worst of both the species - Vampires and Werewolves. The thirst for blood, as well as the pain of turning into a wolf.