"A Rose for Emily" is a bit more experimental with POV. Faulkner uses a first person plural narrator who could be either a group of men from the town, a group of women from the town, or both. Regardless, these are outside narrators. They do not have access to Emily and her secret bedroom. She is a gothic mystery to them.
As such, they are unreliable narrators. They tell the story from a limited perspective: one of rumors, hearsay, and gossip. Their story is episodic and non-linear: it begins with her death and works full circle back to it and Homer's.
"Barn Burning" is told in a third-person POV, but from Sarty's angle. This Sarty-based narration is much more reliable because it gives us an inside perspective: we see into the Snopes family. We have complete access to Sarty and his father's secret (he's a barn burner). In this way, there is no mystery or dramatic irony regarding Abner. The mystery lies with Sarty: will he stay with the family or go?
In sum, both stories rely on "perspectivism": Faulker's technique of shifting narrative structure according to time, place, and space. But "Barn Burning" is much more controlled than the experimental "A Rose for Emily."
Both "Barn Burning" and "A Rose for Emily" are developed through a point of view that enables the story to slowly progress as the reader puts together clues provided by the narrator. These clues, or foreshadowing, are another similarity. "Barn" is told from the perspective of a ten year old boy trying to deal with his family and the community; "Rose" is told from the point of view of the community trying to figure out what to do with Miss Emily. This difference sets up the similarity that both stories employ the theme of the individual vs. the community.
In addition, the main characters, Sarty and Miss Emily, struggle with a loyalty to their fathers which controls and destroys their lives. In the end, both characters end up betraying this loyalty and acting against their fathers. Both main characters also harbor a family secret - Miss Emily hides a dead body; Sarty initially hides his father's arson.
Finally, the settings of both stories are very similar. The settings focus on the decline of the South which was common in many Faulkner works. Faulkner himself lived in Mississippi, and he used his location to create a model for his short stories. Also, Faulkner created the Snopes family and other characters who he referenced in most of his short stories. The common setting and his development of this family contribute to many of the similarities found in his works.