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

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.