eNotes offers a free "how to" guide called How to Write a Compare-and-Contrast Essay in 8 Easy Steps. You might want to check out the link!
Both Faulkner and O'Connery are challenging the culture of the Old South in their respective short stories. In "A Rose For Emily," one of the central issues is that Emily has been made into an untouchable flower by her father, locked up in effect, and made into a "Miss." Misses, we all know, are unattached girls who belong to their fathers in traditional Southern culture. The fact that this tradition is taken to such an extreme is what leads to Emily's psychological detachment from reality and the world around her. In "A Good Man is Hard to Find," the grandmother clings to ideas from the Old South foolishly as the rest of the world progresses. She is annoying and condescending to her old family. At the end of the story, the grandmother is shot, which, it could be argued, is representative of O'Connor's disapproval toward the prideful clinging to of ideals over humanity.
On the contrast side, the characters are dealt with differently in each story. Emily is a tragic figure, a victim of the title of "Miss," which has been attached to her without her permission. The grandmother, on the other hand, is a character who almost makes the reader root for the serial killer. O'Connor herself said that he was her mouthpiece.
I would explore for resources that focus on O'Connor's and Faulkner's treatment of Old Southern ideals in these stories. Start there, and see what you come up with. Good luck!