What other poem can I compare "I Heard a Fly Buzz-When I died," by Emily Dickinson, in terms of the theme of dying or death?
Many of Emily Dickinson's poems depict a theme of death and/or dying. In her poem, "I Heard a Fly Buzz--When I Died," the speaker recalls the sound of a fly in the room as she (assumptive given the poet's gender) wrote out her will.
I willed my Keepsakes – Signed away
What portions of me be
Essentially, the poem is about the things which happen leading up to death.
Likewise, in her poem "Because I could not stop for Death," the speaker is, again, recalling the events which led up to death. As the speaker defines her (again, assumptive) life as being too busy for death, Death (personified) is courteous enough to make time for the speaker. After getting into Death's carriage, the speaker is lead through life (from childhood to the grave--depicting the common belief that one's life may flash before their eyes upon death). While the movement of each poem differs greatly, both are about death and the immediate events which lead up to it.