This kind of stylistic analysis compares choices that two authors make in word choice (diction), imagery, and syntax (sentence structure). Comparing the writing styles of Hemingway and Fitzgerald in these two stories means that you look at specific aspects of the stories. The respective styles of these writers are virtually the opposite, and you can see the difference very quickly just by looking at the length and structure of the sentences each author creates.
Typically, Hemingway relies on simple sentences (one independent clause) or compound sentences connected with coordinate conjunctions (and, for instance, is one of his favorites). The dialogue between characters is also very simple, usually short, and Hemingway offers few descriptive details. Furthermore, he wrote based on an idea he called the "iceberg theory," which refers to the structure of an iceberg: most of it is underwater and unseen; only the tip is visible. Hemingway, therefore, suggests much more than he actually states. As I recall, "The Killers," never quite answers the question of why the men are determined to kill their intended victim; the more important feature of the story is the effect on the narrator.
Fitzgerald, on the other hand, uses much more complex sentences with many descriptive details. His characters are vividly portrayed, often young people from upper middle class or upper class families with a a great deal of free time of their hands. In "Bernice..." reader is probably delighted that the snobby Majorie gets her comeuppance. The plot is resolved satisfactorily.
Look at the authors' choices of words. Are any unusual? Hard to define? Or are they simple words? Examine the length and construction of sentences as well. You'll find, I believe, a stark contrast between the styles of these two authors.