How would the story change if Faulkner told it himself in his own voice, rather than through a narrator who is one of the townspeople?
Since the story is fiction, any narrator telling the story would not be exactly Faulkner. So, I think you are really asking what effect it has to have a first person plural narrator for the story, as opposed to a third person narrator.
I think that a third person narrator would be more likely to be omniscient, meaning that a third person narrator would know everything there was to know about Miss Emily and the events of her life. A narrator who is one of the townspeople can give the reader some information about Miss Emily and what happens in her life, but leaves a great deal to the reader's imagination and speculation. This makes the story richer, I believe. Also, having one of the townspeople tell the story makes the reader feel more as though he or she is part of the story, as though the reader is personally observing Miss Emily and her life. Finally, having one of the townspeople tell the story gives it a kind of "folksy" feeling that makes it feel more authentic.