Hawthorne's tales, whether we are looking at Young Goodman Brown (a short story) or The Scarlet Letter (a novel), almost always contain a moral, and they correspond with the Puritanical leanings of the era in which Hawthorne lived.
Consider Young Goodman Brown: there are the typical fairy-tale morals (the woods are bad, stay on the true path, etc.), but the big lesson comes at the end, when nothing is carved on the protagonist's tombstone because he allowed his skepticism, cynicism, and pessimism to rule his life. This serves as a stark warning, indeed. In The Scarlet Letter, we are given the admonition not to judge others—a biblical value and one that was both controversial and commonly ignored in Hawthorne's era, and those preceding.
In contrast, Poe's stories use history merely as a backdrop or setting, and there are no real morals to speak of. Consider "The Cask of Amontillado," "The Tell-Tale Heart," and "The Black Cat": Poe's motivation in writing each was to intrigue, terrify, and entertain. There are no big life lessons, no preaching of any sort, and no real finger-wagging like we see in Hawthorne's works. In addition, we see characters thrown into a time and place, but neither of those details figure heavily in the outcome of Poe's tales. They just as easily could be set in other eras throughout history.
While Poe and Hawthorne can both be classified as Romantics, their reliance upon history and their appreciation for inclusion of morals varies widely. Both authors' stories, however, maintain appeal even centuries later.