"The Murders in the Rue Morgue" is an interesting mix of styles. When the narrator's just telling the story or when Dupin's talking, it takes on this really grandiose, florid (read: flowery and ornate) style. Check out this sentence, a chunk pulled from Dupin's explanation of how he figured out the narrator's thoughts on the actor, Chantilly:
I knew that you could not say to yourself `stereotomy' without being brought to think of atomies, and thus of the theories of Epicurus; and since, when we discussed this subject not very long ago, I mentioned to you how singularly, yet with how little notice, the vague guesses of that noble Greek had met with confirmation in the late nebular cosmogony, I felt that you could not avoid casting your eyes upward to the great nebula in Orion, and I certainly expected that you would do so. (24)
Notice the sheer number of clauses in this sentence, the extra adjectives – "that noble Greek," "the great nebula in Orion," "nebular cosmogony" – and the use of long, unconventional words ("stereotomy," "atomies," "cosmogony.") All of this goes to revealed how educated Dupin is. But it's also in keeping with the rest of the narration of the story, which is quite elaborate. It's as though, in a story full of complex detail, Poe wanted to use a lot of difficult vocabulary and references to make us slow down and read more carefully, so we won't miss anything important.
Yet, at the same time, there are also points when the writing style is sparse. We're thinking specifically of the reports of testimony in the 32nd through 47th paragraphs of the story. These reports from various witnesses aren't even in complete sentences. The language here resembles mimicking newspaper speak, so it's a little more rat-a-tat-tat than Poe's usual style. But it's also a way of marking that this is evidence, as opposed to a chain of reasoning that we have to follow from beginning to end. These eyewitness reports are pure detail, which means that there are details that we can take and those that we can leave behind. This is quite different from the experience of reading, say, Dupin's dialogue, which is all significant.