In Dr. Jekyll and Mr. Hyde, Dr. Jekyll finds a way to split his evil impulses into a separate human being. In The Picture of Dorian Gray, Dorian makes a pact with the devil that a portrait of his young self while age instead of him.
Both novels are alike in showing the tragic price of trying to either safeguard one's moral purity or one's looks by creating an "other" to bear all the evil. Dr. Jekyll's alter ego Mr. Hyde goes out of control, descending to the murder of Sir Danvers Carew. Dr. Jekyll is shattered by the outcome of his experiment, which he realize too late was a mistake. He ends by committing suicide. Likewise, Dorian Gray realizes too late this his life of self-indulgence without a price to pay has caused him to behave cruelly and left him spiritually empty. He too ends up committing suicide by stabbing the aging and ugly portrait of himself.
The stories different in structure. In Dorian Gray, we as readers know from the start what Dorian has done, while this is a mystery until the end in Dr. Jekyll. Also, in Dr. Jekyll, the point of view is that of the "good" double or mirror image. Dr. Utterson, the story's narrator, is a normative figure who represents the Victorian social virtues and is totally opposed to Mr. Hyde. Dr. Jekyll's letter and his anguish over what Mr. Hyde has done also provide part of the narrative point of view. We do not ever see the story through Mr. Hyde's eyes, however: he is always the evil other.
In Dorian Gray, by contrast, the "evil" double is the point-of-view character. The portrait is the innocent, taking on Dorian's sin in an almost Christ-like way (except, of course, that the picture has no consciousness). In this case, the focus is on what his deal with the devil and creation of a double does to Dorian, the "evil" one, not on what his choice does to other people, as is the case in Dr. Jekyll. It is the perverse and spiritually destructive effects of his choice on Dorian that exposes the mistake he has made. He stabs the his double, his portrait, because of what it has done to him, not other people. Dr. Jekyll, in contrast, kills himself to save other people.