In both "The Cask of Amontillado" and "The Black Cat," Edgar Allan Poe wrote using first person narration. In addition, the narrator or each story commits murder, as well as walling in the victim. The narrator in each story appears to suffer from a mental imbalance of illness of some kind and also shows little or no remorse for having killed someone he knows (and loves, in "The Black Cat"). Each narrator is more obsessed with the details involved with committing the crime than the actual reality of having murdered a person.
The connections between these two narrators allow the reader to recognize the similarity of two of the author's works, which reveal a commonness of theme and other literary elements that exist in Poe's writings. An awareness of the similarities between the two stories causes the reader to also be able to easily identify differences between the two, much like a dramatic foil highlights characteristics in its opposite.
There are differences between the narrators, however. For example, the narrator of "The Black Cat" expresses no real reaction to having murdered his wife, other than the need to conceal her body. The narrator of "The Cask of Amontillado," though, taunts Fortunato when he begs for mercy and, when Fortunato does not respond to the narrator's calls, Montresor says his "heart grew sick." Another difference is that Montresor seems to be able to walk away from the catacombs without thinking about what he has done, while the narrator of "The Black Cat" is tormented by what he has done, since he is obsessed with thoughts of the black cat.