Well done for identifying the use of epiphany by Joyce in these two great short stories. Joyce, in the collection of stories under the title Dubliners, uses epiphany again and again to highlight the way that sudden revelations come to his characters about their state in life and their identity. Interestingly, however, the epiphanies in the two short stories you have indicated, "The Dead" and "Araby," are rather different in the way that they are presented.
The main difference seems to be the speed and sudden nature of the epiphany in "Araby." Note the way that the narrator of this story experiences his epiphany at the same time as the lights of the bazaar that he has visited go out:
Gazing up into the darkness I saw myself as a creature driven and derided by vanity; and my eyes burned with anguish and anger.
The narrator experiences a sudden and devastating epiphany, that brings out an extreme emotional reaction in the boy. However, when we look at the epiphany in "The Dead," we see it is a lot more gradual and much more protracted. Having heard about Michael Furey and his wife's involvement with him, Gabriel Conroy is left to ponder the significance of this revelation on him and his life:
The air of the room chilled his shoulders. He stretched himself cautiously along under the sheets and lay down beside his wife. One by one they were all becoming shades. Better pass boldly into that other world, in the full glory of some passion, than fade and wither dismally with age. He thought of how she who lay beside him had locked in her heart for so many years that image of her lover's eyes when he had toldher that he did not wish to live.
Thus, although Gabriel Conroy definitely experiences an epiphany, it is not so sudden as the epiphany in "Araby." He experiences an emotional reaction, but again this is softer than the immediate, extreme response of the narrator in "Araby."