Both of these poems are about the experience of feeling alone, solitary. But the first, "Alone," seems to focus upon the speaker's formative process, and the uniqueness of it—the fact it is different from that of other people. "Spirits of the Dead," on the other hand, is concerned more with the universal experience of those who are facing death, and their feeling of being cut off from the emotions that animate people who are either not at the end of life or not contemplating the end.
In reading Poe's "The Poetic Principle" I find him leaning towards valuing verse more for its sensory qualities—as a kind of music, in fact—than for its meaning. He defines the concept of truth as somehow opposed to the poetic:
In enforcing a truth, we need severity rather than efflorescence of language. We must be simple, precise, terse. We must be cool, calm, unimpassioned. In a word, we must be in that mood which, as nearly as possible, is the exact converse of the poetical.
Later in the essay he adds that,
To recapitulate, then:—I would define, in brief, the Poetry of words as The Rhythmical Creation of Beauty. Its sole arbiter is Taste. With the Intellect or with the Conscience, it has only collateral relations. Unless incidentally, it has no concern whatever either with Duty or with Truth.
I include these quotes from Poe's aesthetic writings because I believe the two poems selected for comparison both illustrate this primacy of sound and rhythmical beauty over actual "truth." The general impression of "Alone" is one dominated by the flowing, languid quality of the words, and the actual meaning of why the speaker feels this way is somehow in the background, less important than the hypnotic wording, a kind of melancholy melody that continues to haunt us after we have read the poem. In "Spirits of the Dead," the meaning of the poem, to me, seems more concrete, though still showing the centrality of a musical feature in Poe's verse. In the contemplation of death the speaker is alluding, much like Hamlet, to the mystery of what follows death. Of the "breath of God" he says,
How it hangs upon the trees,
A mystery of mysteries!
But beyond the level of not knowing, the speaker also views death in the most negative terms. Of the stars he says:
But their red orbs, without beam,
To thy weariness shall seem
As a burning and a fever
Which would cling to thee for ever.
Despite the differences in theme—the one poem dealing with the formative elements of the speaker's character, and the other dealing with his end-of-life thoughts, what links these poems, as well as their preeminently musical quality, is a pessimistic feeling, one of sorrow or negation. "Alone" abruptly ends with the description of a cloud as "a demon in my view—". That it ends with a dash leaves a feeling of a life truncated, much as Poe's own life actually was.