When answering this question, you must discuss each character’s unique traits and overlapping ones. The grandmother in O’Connor’s story and Connie in Oates’s certainly share similarities and differences based on their characterization.
The biggest similarity is their vanity. This refers to each character’s preoccupation with her physical appearance. For instance, the grandmother dresses in her formal Sunday best for a road trip with her family. She does this so that if she were to die on the side of the highway, anyone who saw her would know “at once” that she was a proper “lady.” This shows that the grandmother is vain because she only dresses up because of how she might be perceived.
Connie is similarly vain in that she enjoys the attention she gets from boys based on her looks. She even stays home from a family event so that she can wash and dry her luxurious hair, which indicates that she values herself over others.
Beyond on obsession with looks, each character also values the appearance of something over actually possessing it. The grandmother, for example, wants other people to think she has manners, but she often lies. Connie wants her friends to think she is enviable and experienced (when she is actually quite innocent). Both characters lie in some capacity to those around them.
However, these characters also have many differences. The most obvious, of course, is their age. Connie is a young teenager, while the grandmother is elderly. Beyond superficial distinctions, the grandmother is responsible for placing her family in harm’s way while Connie sacrifices herself in order to save her family.
The grandmother’s lie about the old plantation, her lapse in memory, and her hysterical tendencies all lead to the family members’ deaths. When the grandmother identifies The Misfit, she immediately pleads for her own life rather than for the lives of her family. This indicates that she remains selfish even after it becomes clear that she has sealed the family’s fate.
On the other hand, Connie has a choice between going with Arnold Friend or waiting until her family returns from the barbecue. Friend promises that choosing the latter will put her family in jeopardy. Instead of potentially endangering the lives of her family, Connie gets into Friend’s car and leaves.
This key difference between the two characters is just one example of how literary figures with similar personality traits can be portrayed differently.