Though both speak of the themes of self and death, Dickinson focuses more on a philosophical exploration of the elusive realities of these themes, while Whitman focuses more on a celebration of these themes.
Both Whitman and Dickinson use nature as a metaphor for human life. Natural themes are prevalent in both their poetry, and both use the animals and places to tell us something about human nature. For example, Dickinson describes a frog in "I'm Nobody" and Whitman also uses animals and creatures.
We need to think of purpose and ambition when it comes to these two very different poets. Dickinson never meant her work to be published, from what we can gather, and sent her poems mostly to close relatives. She only gained fame after her death. Thus the scope of her poetry is restricted to the everyday, the America of the individual and her unique take on it. Whitman, by contrast, deliberately set out to write grandiose works capturing the experience of America as he saw it. He set out to be a poet and have his work published in his lifetime. This results in an essential difference between these two poets and the sphere of their work.
I agree that one significant difference between Dickinson and Whitman is their perspective on self. Dickinson reflects on life as an individual and how that works in life, death, and the universe. Whitman reflects on life as part of a collective, as indivuals who are free to be themselves (or at least they should be) but are also connected to one another.
In my mind, I think that Whitman's poetry and Dickinson's poetry is strikingly similar in their embrace of individual freedom and the ability for the individual to be the author of their own narrative. Where there is significant divergence seems to be in their embrace of a political end to this freedom. Whitman is very open about his belief that individual freedom and endeavor has to strive towards this concept called America and the promises of its fledgling democracy. This becomes part of Whitman's core value system and something highly evident in his writing. Yet, Dickinson does not outwardly embrace this political end, remaining to reside the domain of the personal and introspective. To this end, there is significant difference between them. This is not saying that Dickinson would not have embraced the political ends that Whitman did in his work. Yet, it does bring out another important difference between them. The poetry of Dickinson is very individualistic, while the poetry of Whitman embraces a community. It is here where the differences on more than a political level for a choice within the individual. Dickinson's individually drawn sense of identity is set against Whitman's embrace of American consciousness, one where a political community is forged through individual freedom. It is here where I think that themes and implications of both writers end up taking form and shape. There might not be an ultimatum being forced upon the reader, but certainly there are different implications in each upon which reflection is critical.