How do Emily Dickinson and Walt Whitman differ in their thinking and writing when it comes to modern poetry and understanding God?
This is a difficult, if not impossible, question to answer, but there are some things we can do. First of all, the form of their writing could not be more different, but each mirrors their approach to the world. Emily's world was very small; she lived in a small community and spent a great deal of her time in her house. Her poetry tends to explore the "inscape" --- the tight form and interesting rhymes/punctuation mirror this exploration of her very local world.
Whitman's poetry is quite different. He lived in New York City, a culture that was expanding, highly diverse, noisey, crowded ... you get the picture. His "mystical" vision tries to take in this world and see it as the great democracy where all things and all people blend into one whole. His endless catalogues of all the things he experienced mirror the world that he saw and tried to take in.
Both of them, however, tend to make their own rules. Dickinson's capitalization, punctuation, and rhymes are all her own, and are used under her tight control. Whitman seems to have given up on what we would traditionally recognize as poetry (although he did write some traditional poetry such as "O Captain, My Captain" which follows more traditional form --- I am usually speaking of "Song of Myself" when I talk about Whitman). They each contributed a great deal to the growth and development of modern poetry.
Their ideas about God are much more difficult to compare. Dickinson seems to have an ambiguous relationship with God. In some poems ("Some keep) she seems to have an almost direct, Whitmanesque, relationship with God. In other poems ("Apparently with no surprise") she seems much more skeptical about God. Whitman's God is much less personal, although no less present. Whitman finds God as part of the nature in which everything participates, reminiscent of the concept of the Oversoul that was popular with the Transcendentalists. Dickinson looking inward and finding God there; Whitman looking outward and finding God everywhere.