The previous answer identifies some excellent similarities between the two stories, but here are several more differences.
The setting for the two is quite different. "Jury" is set in Iowa which is not the South--it's the Midwest. "Rose" is, of course, in the Deep South. At first glance this might not seem significant, but one of Faulkner's major themes is the conflict between the traditional old South and the realism of more modern times. Miss Emily represents that Old South and rises up against the "North" (in the form of Homer Barron). Minnie Wright, on the other hand lives on an isolated farm where others don't have the opportunity to study her every move (as the townspeople do Miss Emily's) and is more of a modern woman.
The women's relationship with men is also slightly different. Minnie has an overbearing, stifling husband. Emily had an overbearing father which might have caused her to make such an odd choice for her future fiance.
Additionally, the women's relationship with women is quite different. As far as we know, Miss Emily has no true relationships with other women. Her only servant is a man. She lived motherless with her father before that. Her female relations are against her choices and associates, and the women of the town do nothing to support Emily. On the other hand, while Minnie really had no friends, at one time she was popular (in church), and in the end the women stand up for and protect her--something that the women of Miss Emily's town and family are unwilling to do. They see Miss Emily as an oddity and a subject for gossip.
Finally, the two stories represent different styles of writing. "A Rose for Emily" is a Southern Gothic work--hence, the large Southern home, the creepy atmosphere, and the surprise macabre ending. "A Jury of Her Peers" is modern and realistic. The author, Susan Glaspell, was long an advocate of women's rights; so the story represents a negative stereotype of men and the triumph of feminism. Also, Glaspell based the story (originally the play Trifles) on a real murder case that she had covered as a journalist early in her career. While both stories technically could take place, "Jury" certainly is more believable.
This is a very interesting pairing. On first glance, I see more similarities than differences between these two stories: both main characters are female, both women are "absent" in the story though they are the main focus (Minnie having been taken down to the jail, and Miss Emily having passed away), both women have killed someone (although, in Miss Emily's defense, we don't really know how Homer died), both women are southern women and both stories take place in the south.
Now, one blazing difference is the fact that Minnie Wright did kill her husband. The women in her house find all the evidence that would prove it, although they choose to keep the evidence a secret since they feel somewhat guilty for Minnie's situation and they relate to her woman-to-woman. Emily Grierson probably killed Homer Barron with the "rat poison" she bought from the druggist, but we don't know that for sure. The only people who can speak to that are Homer, Emily, and Toby (Emily's manservant). Two of the three are dead, and the third took off so quickly he was a blur. We don't know that Homer didn't have a heart attack, or that he fell and hit his head while in the tub. However, he most likely was planning on leaving her, thus destroying any reputation she had in tact, and she prevented it swiftly.
Another difference is the financial situation of the two women. Miss Emily was used to fancy living and high-society treatment. Her father was wealthy, her house was in the most affluent neighborhood, and she was the last vestige of the "true south" in her quickly changing town. In some respects, she was naive and sheltered to the point that she couldn't live without some male identity to whom she was steadfastly attached. When her protective father died, Emily sought a father substitute. Unfortunately, Homer did not live up to her standard.
Minnie Wright, however, was not pampered. She did go from the prettiest girl who wore pretty dresses and bows and sang like a bird in the church choir to an isolated farm wife with an abusive husband. Apparently he crossed the line when he broke the neck of the little canary she bought for comfort and company. The bird was found wrapped in silk in a small box within Minnie's quilting things. Ironically, her husband was hung...a similar death suffered by the poor bird.
I suppose that could be another difference. The death of John Wright was by hanging; Homer Baron died of arsenic poisoning.
Neither of the women will be punished by man's law for what they've done. Emily passed on before anyone discovered what she had done, and Minnie's "peers" have decided to hide the evidence of her guilt, thus, she will probably be found "not guilty" and free to return to the home she shared with John Wright.
One more difference may be the way the women deal with their reputations. Miss Emily does everything within her power to preserve her name and position in society; Minnie is "resigned" to what she's done when the men arrive to collect her and her husband. She goes willingly and without incident to the jail.