William Faulkner's story "A Rose for Emily" would have been very different had it been told by Emily herself. The reader would have gained some insight into Emily's behavior, but would have lost the outside perspective of the town's people.
Faulkner is known for being adept at describing both small towns and interpersonal relationships, and "A Rose for Emily" illustrates both. While the story is told in first person, it is not the traditional first person view of a single narrator. The story seems to be told from the view point of multiple people, or at least by a single person who knew of multiple people's opinions on Emily's antics.
If Emily had been telling the story, the reader would have learned what happened during the time between Emily's father's death and when she finally decides to hand over his body three days later.
The reader would most likely have found out how and when Emily decided to kill Homer. The reader is aware that the town thinks Homer is far beneath Emily in social stature, but they apparently have no idea as to Emily and Homer's actual relationship. When Emily buys the men's outfit and toiletry set, the townspeople assume it is for their marriage, but when Homer disappears, no questions are really asked. From Emily's point of view we would have intimate knowledge of her feelings towards Homer.
Another character we might have gained more insight into if Emily were telling the story is her servant, Tobe. Tobe is with Emily on a day-to-day basis and must have known of Emily's actions concerning both her father and Homer. With Emily as the storyteller we would finally know what she had done or given Tobe to ensure her actions never came to light in the small town.
Emily would most likely have discussed her view on the people of the town. When Emily sees the men sprinkling lime around her house in order to conceal the odor rather than confront her, she must have had many emotions. She could have been angry or possibly scared that her actions would be found out and the body would be found.
Emily was cut off from the world at a young age by her father. This caused her to become quite reclusive after his death. A story told from Emily's point of view would show how she spent her time without much contact from the outside world. We would know why she continued to shy away from the people in town.
The reader is left with many questions at the end of the story that could have been answered had Emily been telling it. But in many ways the story being told from the town's point of view is a good thing, as it shows interactions between people in a small southern town. We would have lost the ability to know how people talked about Emily, and their opinions on her behavior.
Emily most likely would have felt that everything she did was quite normal, even though she did know that she needed to conceal Homer's body, so she must not have been truly insane.