The first most obvious contrast between the two short stories is authorial style. Hemingway writes short sentences that are enhanced by metaphor, symbolism, and imagery. His sentences tell as much about the story indirectly as they do directly. For example, Hemingway's opening description of the deaf old man provides a metaphor to support his thesis that life, after the verve of youth is gone, is "nada" and "nothing." It also provides foreshadowing of the old waiter's soliloquy and solitary experience with seeking dignity and lying in a sleepless bed, which so sharply contrasts with the young waiter's warm bed.
Faulkner, on the other hand, writes long sentences, for example, consider his second paragraph:
He had listened to it for years: the long legend of corncribs rifled, of shotes and grown pigs and even calves carried bodily into the woods and devoured, of traps and deadfalls overthrown and dogs mangled and slain, and shotgun and even rifle charges delivered at point-blank range and with no more effect than so many peas blown through a tube by a boy—a corridor of wreckage and destruction beginning back before he was born, through which sped, not fast but rather with the ruthless and irresistible deliberation of a locomotive, the shaggy tremendous shape.
While Faulkner's sentences make use of imagery, "the ruthless and irresistible deliberation of a locomotive," they rely much less on metaphor and symbolism than do Hemingway's sentences.
The most obvious way in which the stories are comparable is in the tone. Both stories express existential angst with tones of despondency and existential despair, though Faulkner's story adds a raw brutality of tone: "of traps and deadfalls overthrown and dogs mangled and slain, ...."
It was all a nothing and a man was a nothing too. It was only that .... (Hemingway, "A Clean, Well-Lighted Place")
He was ten. But it had already begun, long before that day when at last he wrote his age in two figures and he saw for the first time ... the tremendous bear with one trap-ruined foot .... (Faulkner, "The Bear")