In both stories, the protagonist lives in a dreamworld. For the young adolescent boy in "Araby," the dream revolves around his friend Mangan's unnamed older sister. The narrator develops a crush on this young woman, though he has barely spoken to her. She represents for him the possibility of a better, more romantic life than his dull existence in Dublin. His adoration of her from afar becomes a "chalice" or vessel in which he can pour all his heightened emotions. When she tells him of her regret at having to miss the bazaar, Araby, the bazaar attains a special, exotic romance is his mind. He is obsessed with the idea of going there and buying her a gift.
Likewise, Emily builds a dreamworld around Homer, a Yankee foreman who comes to town. They get involved, but when he wants to leave, she poisons him and keeps his corpse in her bed for companionship for years until she dies.
For both protagonists, a fantasy is preferable to a reality that seems unbearably lacking in romance. The narrator of "Araby" doesn't know Mangan's sister well enough to really be in love with her: he is in love with a fantasy image he has devised in his mind. Emily also does not really love Homer but loves the idea of having a lover: you don't murder people you truly love.
At the end of the story, Araby's narrator realizes he has been deluding himself. Emily, however, clings to her fantasies at all costs.