There are a few things to consider. In drama, the script reveals the story, but the script consists of dialogue, stage directions, etc. Also, the dialogue must be memorized and delivered by the actors. So there are levels in drama that do not exist in reading literature because of the actors' performance, which is how the audience will respond to the work. The audience interacts with the script, then, in a way that is interpreted by the director and the actors. Plus, the audience most likely does not have any knowledge of the story or what is going to happen, because usually the audience has not read the play before the performance. This is not always so, however.
The reader responds to the text solely on his own. There is no actor, no director, no stage directions. The text is the "script" but the reader is the only interpreter. The reader is left to imagine what the characters are like on his own, whereas in drama, the characters are revealed through the actors' acting and the director's directing.
In the case where a person has read the play and then sees a performance, the two are combined, such as with Shakespeare's plays. Or, sometimes one will view a play or a movie after having read the work. This can be disappointing because things that are written down do not translate to being performed, so playwrights, screenwriters, directors, etc. do not use all of words when translating the work to the screen or to the stage. Also, essential elements of plot can be changed. That is why one is often disappointed by a screen or stage adaptation of a novel, for example.
You have to take these considerations and put them into an essay. Make sure to use examples to specific works, if this is a requirement for the assignment. If you are looking for a fairly modern example, may I recommend Dogeaters by Jessica Hagedorn. There is the novel, which was written first, but the author is also an actress and a playwright, so several years after writing the novel, she turned it into a play. The play is quite different from the novel, the characters are not all the same, and it was quite a challenge for her to translate her fiction into performance. You can do some research on this. Since you are in graduate school, I am guessing that you will have to use some concrete examples.