One interesting approach to the question is to consider the lives and works of the three men in relation to Transcendentalist philosophy.
Certainly each believed in and lived according to the generally acknowledged central ideas of Transcendentalism—the divinity of humankind and nature, the resultant goodness of the two, the corrupting influence of society, and its tendency to erode an individual's self-reliance. By looking at the works and lives of these three men, one is able to see the nuance in their visions of Transcendentalism.
Emerson was the intellectual, the writer and lecturer on history, religion ("The Divinity School Address" and "The Over-Soul"), and the unique character of the American mind ("The American Scholar"). His was widely considered to be an expert on a range of topics, and he even dabbled in the controversial, including criticism of American slave policy. But his life was the life of an intellectual; his divine spark saw fit to light a way for others.
And they followed. Both Henry David Thoreau and Walt Whitman brought their own distinct views to the movement. Thoreau's experiment in living at Walden Pond (Walden; or, Life in the Woods), his own protests of American slavery ("Civil Disobedience"), and his general dedication to a life appreciating and remarking on the wonders of the natural world all speak to a Transcendentalist illumination that is perhaps more literally "down to earth" than Emerson's intellectualism.
Whitman's work Leaves of Grass, both in its very "nature" and title (altered and republished again and again, the pages truly like blades of grass in a field), reflect the wonder at the natural world central to Transcendentalism. And in Whitman's bon vivant nature, his refusal to adhere to social norms, and his resistance to poetic standards, one is able to discern a dedication to the personal independence and recognition of the divine spark that mark Transcendentalist thinking.
Emerson lit the Transcendentalist way with his clubs and lectures and essays. His was an intellectual approach to the movement. Thoreau followed with his experiments in living and observations of the same. He was constantly experimenting with the ideas of the movement, turning theory into reality. Whitman carried the movement into the very nature of his greatest work and the markedly independent life he lived.