When you think your essay's done, make sure you give it one more pass, checking for errors in both content (faulty arguments) and form (bad grammar, spelling, etc.). No doubt your teacher will be grading you on completeness, and an essay doesn't exactly seem done if it's riddled with errors. It might be especially helpful to get a second set of eyes; you could ask your parents, peers or even a TA (in a college course) to take a look at your arguments and make sure they stand up to scrutiny. After that, congratulations! You've got a compare and contrast essay on your hands. Was that so bad?
In terms of working on this particular prompt, I think you are going to have to do much of the legwork yourself. Guidance and input can be given, but the bulk of the work is going to have be self initiated. I think a good starting point would be to discuss the mood of each poem. What general sentiments or feelings are brought out by reading each? This might involve you reading the poems to yourself, aloud or silently, a couple of times in order to grasp where Dickinson's mind is and how she attempts to connect to the reader. Another mode of discussion could be how death is characterized in each. What does death "feel" or "look" like in each? Then, ask yourself how different this might be from the traditional conception of death. What Dickinson is saying about death in both might be another topic to pursue. Finally, I would examine the theme, or overall message, in each. These might be good starting points to show points of convergence and divergence in both poems.