McGowan Dickinson Whitman

Perhaps the most obviously shared quality between the two poets is their shared interest in the existence of immortality. Whitman believes that the human soul is one and the same with the body. He sees the body as an essentially eternal enigma, which lives on through the nutrients nature extracts from it. "I am the mate and companion of people, all just as immortal and fathomless as myself", suggests that, like Emerson, Whitman has a pantheistic world view. Whitman sees all things and all people as interconnected parts of a universal whole. Dickinson has a somewhat different, more cynical take on eternity as seen in "Because I could not stop for Death". Like Whitman, Dickinson sees death as a sort of entrance into immortality. 
Because I could not stop for Death
He kindly stopped for me
The Carriage held but just Ourselves
And Immortality.
From this stanza, we see that Dickinson equates her own death with falling into some kind of eternal abyss. Throughout the poem, Dickinson characterizes her newfound eternal existence as somewhat passive and disillusioned. "Since then 'tis centuries and yet Feels shorter than the day", shows us that the speaker's experience of eternity has caused her to lose concept of time and space, leading neither a negative nor positive existence. She simply is. 
Another similarity between the two authors, also regarding death, is that they both focus on death in conjunction with nature. Part 49 of "Song of Myself" exemplifies Whitman's take on this matter.
"And as to you Corpse I think you are good manure, but that does not 
offend me, 
I smell the white roses sweet-scented and growing" 

This shows that Whitman sees our existence as circular. That is, we are born, we live, and once we die our nutrients ultimately contribute to nature, which in itself is universal. In "I died for Beauty--but was Scarce, Dickinson also explores the concept of death in nature. "Until the Moss had reached our lips --/And covered up -- our names –". Here, Dickinson sees nature's interaction with death as a mechanism for anonymity and, in short, the idea that we will all be completely forgotten one day. Dickinson seems to hold that this is a direct product of nature, which makes sense, as this idea of moss covering up our names is probably a reference to time and decay.  

Finally, the two authors clearly share a very transcendentalist interest in the self. Both of them have a very strong tendency to write in the first person about their own experience of life. For Whitman, this is a celebration of himself and his universality. This is made very apparent through the first few lines of "Song of Myself": I CELEBRATE myself, and sing myself, 

And what I assume you shall assume, 
For every atom belonging to me as good belongs to you.

What Whitman is essentially saying here is that every single human being, organism, and anything that exists is a part of a universal whole, which is why it should be upheld simply because it is. Dickinson, on the other hand, uses her self-interest in an opposite sense: introspection. While Whitman is interested in how he factors into the universe, Dickinson is interested in how she factors into herself. Dickinson often does this by narrating her own proverbial death, such as in "I heard a Fly buzz--when I died". This poem is specifically mournful as it deals with the ultimate loss--the loss of oneself. 

With Blue -- uncertain stumbling Buzz --
Between the light -- and me --
And then the Windows failed -- and then
I could not see to see --

This final stanza refers to death as a very personal experience. The presence of the fly is imposing and seems to interrupt Dickinson's final experience of herself. This injustice might cause a reader to view the external as a distraction to what is ultimately important--the self.