In both novels, a main character—in Wuthering Heights, Heathcliff, Dorian in The Picture of Dorian Gray—uses his power to indulge his dark impulses.
In Heathcliff's case, his dark impulse is to get revenge on both Hindley and Linton by destroying their families. He believes that both men separated him from Catherine. In Dorian's case, it is to life a live of debauchery without showing the effects of it on his body.
Both men are able to achieve their goals, though in both cases, the means are mysterious. Heathcliff, who disappears for three years after hearing Catherine say she will marry Linton, comes back a mysteriously changed man. From a degraded farmhand, he has become a well-dressed, well-to-do, and polished gentleman. While the surmise is that he entered the army, we are never told what happened during those three years.
Dorian is also able to achieve his goal. His means are mysterious in a different way: somehow, supernaturally, his portrait ages in his stead.
Both men engage in destructive acts: Dorian cruelly rejects Sybil, who commits suicide, while Heathcliff destroys Isabella's life by marrying and abusing her. Heathcliff kills Isabella's dog while Dorian murders Basil. Heathcliff treats young Catherine Linton cruelly when he has her in his power, in one scene slapping her face repeatedly.
Both men, however, give up their dark ambitions in the end. Dorian stabs his portrait in distress, killing himself by this act. Heathcliff, realizing somehow that he will soon be united in death with his beloved Catherine, loses his will to destroy the love growing between the young Catherine and Hareton.
Both novels condemn the behavior of their protagonist. What makes each novel compelling, however, is that we can identify to some extent with the protagonists' desires, if horrified by their actions.
The two novels differ, however, in that Wuthering Heights shows the childhood that created the monster inside Heathcliff, while Dorian comes to the reader fully grown (if not yet 20), with no childhood backstory to explain his motivations.