The story of Dracula would be different if there was only one traditional narrator, first person protagonist, in the sense that the tone of the story would change, the feeling of realism would not be as strong and if the narration was first person from a protagonist the characters would have armour against death.
If the story of Dracula was told through a traditional narrator, it would lose its mysterious feel. This would happen because there would be details that the narrator might describe in first person, that may be omitted in epistolary form because the character forgot, or chose to leave out the detail for some reason.
The loss of mysteriousness would then lead into the loss of realism in the story. For example, in the story, it could be argued that you get to know some of the characters personally, supported by the fact that the readers get to read the characters personal diaries. The newspaper clippings and diaries help give the story more realism, a form of evidence that the tale actually happened within the universe in which the story takes place. While the story of Dracula, when transcribed in the first person, would resemble more of a tale being told by a friend at a party, it might be true, or it could be a complete lie where there is no solid evidence as to whether or not it really happened.
The tale of Dracula told from first person, would also suffer another consequence. The character telling the story would have a type of shield against death, because without this, how can the character tell the story if they are dead? Unless the author introduces some form of reincarnation or afterlife where the dead can interact with the living, such as in the Percy Jackson series where the protagonist tells the tale. Whenever Percy was in mortal danger the suspense was lost because if he didn’t survive, there would be no point doing anything else in the book.
Mystery, realism, and unpredictability of the characters’ fate add to the interest of the novel. If the tale of Dracula was told in a traditional first person protagonist narrative form, it would have less mysterious, have less realism, and would give the protagonist a sort of armour against death.