I think that "The Cask of Amontillado" is interesting because it is based on a true story. Poe read a newspaper article about a body found walled up in a crypt in Italy, and that seems to have gotten his wheels turning. I wonder how true his version was?
As ask996 mentions, the narrators of both stories are key elements as they are unreliable. Through their narration, as well, one of Poe's techniques known as arabesque is utilized. This is a technique in which a motif is drawn and redrawn as it recurs in the mind of the irrational narrator. For instance, Montesor in "The Cask of Amontillado" continually stresses the niter and the dampness as harmful to Fortunato: "We will turn back..." he says, having no intention of doing so. Likewise, in "The Tale-Tell Heart," Poe's irrational narrator insists, "I loved the old man."
The setting is more significant and more developed in "The Cask of Amontillado." Montresor's taking Fortunato deep into the catacombs emphasizes the cruel isolation of his being buried alive. No one will hear his suffering and his screams. Also, the religious history and implications of the catacombs provide a bitter irony in the story as Fortunato is left to "Rest in Peace."
The stories are both illustrative of their Gothic nature. They both involve elements of death, darkness, horror, coldness, dampness, fear, obscurity, mystery. They give you the personal journeys of two men going from sanity to insanit, and gives you the "trainwreck" ride of a lifetime how the action picks up until the tragedy in the end.
Other elements, such as the ones mentioned in the previous posts also make them actually more similar than different, when you really look at it.
Both of these tales have a narrator who is bent on harming another human being. And, both narrators seem to give rather petty or ambiguous reasons as to why they are going to do that harm. In "The Tell-Tale Heart," it is the old man's staring and vacant eye. In "The Cask of Amontillado," is is the "thousands of injuries" and "insult" that Fortunado had given Montresor over the years. Both narrators are telling the tale first-hand, and end with their victims' deaths. Both narrators have unusual ways of disposing of the bodies, burying them both--one in stones, one under floorboards. Both planned out their scheme beforehand, and took precautions to not be caught. In "The Tell-Tale Heart" the narrator took his sweet, stealthy time in sneaking silently and undetected into the man's room. In "The Cask of Amontillado," the narrator had the spot picked out beforehand, and commanded all of his servants to not leave the house, which ensured that they "absconded to make merry" during the festivities, so that he wouldn't have witnesses.
The differences between the stories are that the narrator in "The Tell-Tale Heart" gets caught by the police, because of his guilty conscience that manifests itself through the beating heart. Montresor, on the other hand, does not get caught, and lives out his days with no one knowing. Montresor is not burdened by accusations of madness like the other narrator is; in "The Tell-Tale Heart," it seems like the entire purpose for telling the tale is to prove that he isn't insane. Montresor, on the other hand, just seems to want to tell the tale for the tale's sake, not to prove that he is sane. In Montresor's case there is no auditory hallucination of the beating heart to force him into confession; very little evidence of a guilty conscience is seen in Montresor.
I hope that those thoughts help to get you started; good luck!
I guess I'll state the obvious point of comparison--since they're written by the same author, they share a similar diction and style in the actual writing. All the other elements mentioned above are more significant, but reading these two Poe selections--as well as any others, actually--his particular diction (word choice, vocabulary) is recognizable. That speaks of similarity and comparison.
Other editors have summed up the key similarities between these two masterful gothic tales. The major similarity is of course Poe's masterful use of the unreliable narrator. This point of view takes a first person narrative but key to its success is the way in which the attentive reader is not entirely convinced by what is written and begins to suspect that the narrator is unreliable in what he or she says and reveals. This is certainly true as we read both of these tales - both Montesor and the narrator in The Tell-Tale Heart show themselves to be deeply disturbed and violent individuals who do not know the depth of their own twistedness.
Both “The Cask of Amontillado” and “The Tell Tale Heart” by Edgar Allen Poe have first person narrators who seem to be sinking into the dark mists of madness. This means that as readers we must be skeptical about the information we receive from the narrators.
Also both of these stories have characteristics that may or may not have happened, leading to an even greater mysterious element.