Walt Whitman's poetry expresses an enlarged vision that encompasses the universe in a broad way, in expansive outward gestures and long poems. In contrast, Dickinson's poetry is interior, dealing with her states of mind, and is short and compact.
In the opening lines of Whitman's "I Sing the Body Electric," in Song of Myself, he reveals an embrace of the many, a vastness of vision, describing those he loves as no less than armies:
I sing the body electric,
The armies of those I love engirth me and I engirth them
This is highly energized, electric verse. But if Whitman wants to sing his feelings in a way that includes all the world, Dickinson, on the other hand, eschews the grand stage. In "I am Nobody! Who are You?", she writes a compact poem in favor of a reclusive vision:
I’m Nobody! Who are you? Are you—Nobody— too? Then there’s a pair of us! Don’t tell! they’d advertise—you know! How dreary—to be— Somebody! How public—like a Frog—To tell one’s name—the livelong June—To an admiring Bog!
It is hard to imagine Whitman thinking it "dreary—to be—somebody." If Dickinson was nobody and glad of it, Whitman thought his being encompassed everybody, the entire universe.
However, Walt Whitman and Emily Dickinson both had an interest in death that marks them as 19th century poets, and both used everyday imagery, such as of hair or a house, to describe death's presence among the living. Whitman, in "Song of Myself," writes of grass as the "the beautiful uncut hair of graves."
In with a similar vein, Dickinson writes in "Because I could not stop for Death" of a gravestone as the roof a house:
We paused before a House that seemed A Swelling of the Ground—The Roof was scarcely visible—The Cornice—in the Ground
Perhaps most importantly, both were bold innovators with sharply distinctive voices. Dickinson's poems, with their many dashes and short verses and simple words packed with emotional intensity, are startling in their originality. Whitman also innovated, developing his own style of free verse that is unmistakably his own, with passion sizzling through his words.