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.

One point of comparison, of course, is that both Emily Dickinson and Walt Whitman are considered today by many to be the founders of modern American poetry. See, for example, the video program and printed anthology with the title Voices and Visions. (The link is provided below.) Both poets also lived and wrote in the northeastern United States in the latter half of the nineteenth century.

Other points of comparison and contrast include:

Intro- and extroversion -- Dickinson's voice is quiet, sometimes even a little self-effacing (as in her poem "I'm nobody"), whereas Whitman's is loud, expansive, and often boastful.

The natural world and beyond -- Both poets often reflect on their experiences with and their relation to the natural world, and both move from concrete observations of nature to metaphysical or spiritual reflections.

Line length, meter, and structure -- Dickinson's poems are more regularly structured that Whitman's (often following the structure of Protestant hymns), although hers, too, have their own unconventional traits, including punctuation.

If you are completing an assignment on this topic, you may want to identify and systematically discuss one or two specific poems by each authors. Generalizations, like what I've given in this post, are fine, but examples go a long way toward making a good argument. If this topic is for a longer paper, you may even be interested in exploring Dickinson's disapproval of Whitman's subject matter and style. There are also many internet links (a couple are interested below) that may point you in further directions.

What are the differences between Walt Whitman's and Emily Dickinson's poetry?

Walt Whitman and Emily Dickinson are considered to be, not only the two best poets of the nineteenth century, but also the two best poets that the United States has ever produced. Of course, this, like so much else, is debatable.

Whitman's poetry is characterized by a lack of economy, which is unusual in poetry. Leaves of Grass, his best-known collection of poetry, was first published in 1855 and was edited and re-released several times, sometimes including new material. These editions show print that sprawls out onto the page and barely stays within its borders. On the other hand, Dickinson's work was sparse. Editions of her work are characterized by pages of empty space. Most of her poems are only a few stanzas long, each with (usually) four concise lines, while Whitman's poems went on for pages.

Whitman wrote "Leaves of Grass" with the admirable, though naive, belief that a poem which regaled the nation's diversity and celebrated the humanity of all, could save the country from going to war. His work, to quote "Leaves of Grass," sought to "contain multitudes."

On the surface, this is not what Dickinson appears to be doing. Though both Whitman and Dickinson were rather insular—Whitman had only been out of the United States once to travel to Canada—Dickinson had rarely left her family home in Amherst, Massachusetts. What little we know about her life emerges from the letters she wrote to family and friends. We also know that she was fond of gardening and studied botany. She expressed her love for flowers and plants in her poetry. 

The trouble with Dickinson's work is that the reader cannot be sure if her depictions of simple matter, such as flowers, is meant to be read literally (highly unlikely) or if she used these elements metaphorically. Numerous flower poems have been read as evidence of her interest in sexuality. This is not so far-fetched, given that flowers are the sexual organs of plants, which Dickinson would have known. What is interesting is that, while Dickinson may have conveyed these messages in a subtle form, Whitman unabashedly talked about sex in his "Calamus" poems, released in the second edition of Leaves of Grass in 1860.

In sum, Whitman and Dickinson produced work that was vastly different in style. Arguably, Dickinson worked more with figurative language than Whitman, allowing her work more mystery. 

Compare the poetry of Emily Dickinson and Walt Whitman.

Even though both authors are the founders of New American Poetry, a movement which pulled away from the Romantic authors' strict structure, Whitman and Dickinson write very different poetry. While Whitman often writes in free verse with no standard meter or rhyme scheme, Dickinson follows rhyme patterns and usually a very strict meter (almost all of her poems--because of their meter--can be sung to the tune of "Gilligan's Island").

Another difference is that Whitman stresses an undeniable optimism in mankind.  He follows Emerson's view that man cAN be self-reliant and find answers within himself.  His "I Hear America Singing" praises the common worker. In contrast, Dickson's poetry is often very personal and discusses inner struggles.  Her "Heart, we will forget him" demonstrates this theme, and much of her poetry seems unconcerned with one's role in the community (most likely because of her reclusive nature).

A similarity between the two poets is that both veered away from the Romantic poets' traditional view of God or a Higher Being.  Whitman stresses an Emersonian Oversoul or a "god within one's self," while Dickinson is more concerned about earthly emotions and relationships.  Admittedly, both poets include aspects of spirituality in some of their poetry, but those spiritual elements vary drastically from the Romantic poets' themes.

The previous answer is quite funny.  I think that there can be many points of convergence and divergence between both.  The primary point of similarity in my mind between both thinkers is a praising of the subjective experience.  This idea was of vital importance in the writing of Dickinson, who was driven to explore the different valences of the individual and an existing social order.  At the same time, Whitman was part of the Transcendentalist Movement, which located the subjective experience as essential to understanding the nature of truth and the individual's quest for it.  Whitman was firm in his belief that the American Historical experience and its political expression of democracy represents something worthy of praise.  Dickinson was more personally driven, more subjective, than the expression of this political ideal.

What are the differences between Walt Whitman and Emily Dickinson?

Much of this is going to come from your own perceptions and your own analysis.  I think that there is a similarity to locate human truth and understanding through the worship of the subjective.  Yet, within this, I think, lies a fundamental difference.  Whitman explores the subjective in the hope of demonstrating an outward and explicit worship of the community.  Whitman is unabashed in how he believes that what it means to be "American" lies in a shared consciousness.  While the subjective is a realm to be harvested, it is one to be shared with others.  In this, Whitman does not believe that the individual is meant to remain isolated.  In my mind, Dickinson does not seek to "go there."  She explores her own sense of identity and her own place in the world.  If the reader connects with it, the bounds of the community might be established.  I don't see Dickinson seeking an active embrace of the community and its representation in the political dimension as Whitman stresses.  While Whitman could not fully embrace the reality of isolation in the American dynamic, I think that Dickinson is quite content with this reality.  In Whitman, the exploration of a positive view of liberty, the political and social expression that allows individuals to "do great things" is matched with Dickinson's conception of "negative liberty," the reclusive journey into the "inner citadel," to quote Sir Isaiah Berlin, in which one seeks to be left alone.