The biggest similarity the stories share are their surprise endings. In The Necklace Mathilde is surprised to learn that she has become destitute because she replaced a fake diamond necklace with a real one. In The Cask of Amontillado Montresor surprises Fortunato and the audience by finding retribution in the live burial of Foruntato.
The stories also have characters who express intense feelings of jealousy and entitlement. Mathilde is jealous of everyone who is wealthier than she is; she feels she was born to the wrong class. Montresor feels entitled to enact his gruesome retribution plot against Fortunato for the "thousand injuries" which were never named. He also gives off a jealous tone toward Fortunato as well when they are speaking at the carnival.
Both stories are good examples of distinct narrators and voice. In the Cask of Amontillado Montresor is the narrator and he is very unreliable as our first-person narrator. The Necklace is told from the third-person limited point of view, and while that is different we do get the clear distinction between each story.
These two authors are similar, I believe. Fortunato becomes a prisoner in 'The Cask of Amontillado'-he is walled up by Montresor. But Montresor is also a prisoner because he is unable to let his desire for revenge go-it consumes Montresor. In 'The Necklace' by Guy de Maupassant, matilde is a prisoner to vanity and selfish desires-she wants a necklace, and chooses to spend her entire life foolishly working to replace the necklace, because Matilde believes the necklace is the most wonderful thing in the world. Through this story, the author is asking us what it truly important-is it an inantimate object, such as a necklace, or is it life, such as Fortunato and Montresor's life?