What makes Heathcliff a byronic hero is the fact that Cathy did not return his feelings the way he had wanted–she married Edgar for social staus and money, and in Heathcliff’s mind, rejected him. Which caused him to become the vengeful man that he is. Also, Heathcliff is not a murderer, though he has done much. Also, despite how horrible Heathcliff is, he never would have let Cathy go, never would have chosen power over her, not like Rumpelstiltskin did.
Rumpelstiltskin at first started with good intention until he began killing from left and right, and for no true reason. He killed a man for accidently injuring his son, he killed a maid because he was paranoid, killed his wife in a bitter, jealous rage, twice chose power over the people he loved, and has terrorized people simply because it amused him.