Compare Heathcliff's and Ahab's obsessions.

Ahab is obsessed with finding and killing the white whale that bit off his leg on a prior expedition. He identifies the whale with evil. He is willing to sacrifice his entire crew and the profitability of the voyage to his single-minded quest to destroy the whale.
Heathcliff is obsessed with getting revenge on the Earnshaw and Linton families, who he blames for dividing him from Catherine and trying to destroy him. Both Ahab and Heathcliff are trying to address wrongs from the past that were done to them. Both have been hurt and lash out harshly in response.
Both men also are driven by what we might call a metaphysical aspect of their obsession. For Ahab, his quest is driven by more than a desire to destroy Moby Dick, a particular whale. Moby Dick represents to him the malevolence of the cosmos, and it is this that Ahab wants to fight back against and destroy. Likewise, Heathcliff is driven by his desire to connect with the ghost or spirit of Catherine, which he believes haunts the moors. She torments him, which is why he reacts with such vehemence when Lockwood tells of his dream of Catherine knocking at the window, trying to gain entry to Wuthering Heights.
In the end, however, Heathcliff is able to attain a cessation of the desire for revenge. This comes from a foreknowledge that he will soon be reunited with Catherine, and it allows him to leave the young Cathy and Hareton to pursue love without interference. On the other hand, Ahab is driven to destroy himself and all of his crew but Ishmael because of his obsession.