There are a number of options that could be selected in answering this question. What is obvious about "Alone" by Poe is that it is a poem is written in the first person, with the speaker being the person who talks of their own experiences of growing up and how they felt different from the first. The last line in particular is a sinister climax of the "demon" that the speaker saw at a critical moment in his life, and how this presumably perpetuated his feelings of difference and even worse, suggests that he might have engaged in demonic acts as a result of the appearance of this "demon."
A similar poem that could be used to compare and contrast "Alone" would be "Porphyria's Lover" by Robert Browning that is written, like "Alone," in the first person, but is a dramatic monologue in that it tells a specific story and recaptures a particular experience. What links it to "Alone" is that both poems expose the mind and thinking of a figure who is on the fringes of society and clearly rather a dangerous person. Note how this is reflected in "Alone":
From childhood's hour I have not been
As others were; I have not seen
As others saw; I could not bring
My passions from a common spring.
The beginning of this poem clearly establishes the profound difference of the speaker and cites his inability to find any commonality in terms of seeing or being with his fellow human creatures. In the same way, "Porphyria's Lover" is a poem that gives the reader an insight into the mind of a man who is clearly insane to some degree, as he feels the only way he can possess his lover is to kill her. This poem would therefore be an excellent choice to use to compare and contrast with "Alone." You might like to look at other dramatic monologues by Robert Browning, or perhaps by Carol Ann Duffy, such as "Education."