What an interesting question. I must admit, I don't automatically connect these two texts together when I think of Poe's fiction. Clearly, there appear to be more differences than similarities, such as the way in which one is a poem and the other is a short story, one is written in the first person and the other is written from the omniscient point of view. However, having said this, I think one connection we can make between them is the way in which both texts concern man's attempt to escape death and its impact, and the depressing failure with which such escape attempts are met.
In "The Raven," for example, the speaker is trying to desperately get over the death of his beloved Lenore. However, the appearance of the raven and the sinister way in which the speaker tortures himself by expressing his own doubts and his own grief about her death clearly indicates that the impact of her death upon the speaker is not something that he will be able to shake off lightly and forget about. Consider how the poem concludes with a description of the raven and its impact on the speaker:
And his eyes have all the seeming of a demon's that is dreaming,
And the lamplight o'er him streaming throws his shadow on the floor;
And my soul from out that shadow that lies floating on the floor
Shall be lifted--nevermore!
Clearly the grim realities of death are something that will haunt the speaker for the rest of his life. They are not soemthing from which he can escape.
In the same way, "The Masque of the Red Death" concerns the futile attempt of Prince Prospero to cheat death and escape the plague that is ravaging the country. Note the scenario that is given:
When his dominions were half depopulated, he summoned to his presence a thousand hale and lighthearted friends from among the knights and dames of his court, and with these retired to the deep seclusion of one of his castellated abbeys... The courtiers, having entered, brought furnaces and massy hammers and welded the bolts. They resolved to leave means neither of ingress or egress to the sudden impulses of despair or of frenzy from within... With such precautions the courtiers might bid defiance to the contagion.
The story is of the attempt to cheat death, and of its ultimate failure, as death himself, personified in the figure wearing the mummer's mask, appears as the masque and lays waste to all inside. The final, apocryphal paragraph of the tale makes clear the way that death cannot be cheated or gainsaid by its reference to the "illimitable dominion" of "Darkness and Decay" over this land.