How are the poets Walt Whitman and T.S. Eliot similar and different in their writing styles?

Whitman and Eliot are similar in that their works, such as Whitman's "Song of Myself" and Eliot's "The Wasteland," are accounts of the way the individual reckons with reality. Whitman's poetry describes the idiosyncratic way in which one individual perceives reality, including the reality that comes from the senses, and makes sense of it. He writes in "Song of Myself":

"Houses and rooms are full of perfumes, the shelves are crowded with perfumes, /I breathe the fragrance myself and know it and like it, /The distillation would intoxicate me also, but I shall not let it."

From the perception of perfumes, Whitman thinks about how reality will affect his consciousness and how he will interpret it. 
Similarly, Eliot writes of sensory perception in "The Wasteland:"

"'You gave me hyacinths first a year ago; / 'They called me the hyacinth girl.'— / Yet when we came back, late, from the Hyacinth garden, / Your arms full, and your hair wet, I could not/Speak, and my eyes failed, I was neither Living nor dead, and I knew nothing."

Both poets use incoming sensory information and filter this information to make a decision about the ways in which their consciousness will interpret this information and make sense of it.
However, Whitman's perceptions of the world around him lead him to develop an essentially hopeful and cohesive view of the world around him. He writes, for example,

"The delight alone or in the rush of the streets, or along the fields and hill-sides, / The feeling of health, the full-noon trill, the song of me rising from bed and meeting the sun."

In his vision of the cosmos, people and nature are one, and he feels unified with the physical reality around him. His vision is also a very American one. He feels at home in the world and with "the grass I love," and he experiences spiritual regeneration from his interaction with the world.
Eliot's perceptions of the world around him, on the other hand, lead him to have a fractured and uncomfortable view of the world. He writes, for example, of "A heap of broken images, where the sun beats, / And the dead tree gives no shelter, the cricket no relief." While Whitman finds comfort in nature, Eliot feels only discomfort and a sense of alienation. While Whitman's view is distinctly American, Eliot's vision is rooted in the destroyed Old World. He writes of London that it is an "unreal City, / Under the brown fog of a winter dawn." Eliot's world is one of unreality and spiritual deadness, while Whitman's world is one in which he enjoys solidarity and spiritual renewal.