Both Nobel Prize-winning writers, their lifetimes spanned almost exactly the same years. Their writing styles were dramatically different, but the outdoors figured prominently in their lives and in their writing. Hemingway wrote about both hunting and fishing whereas Faulkner, to my knowledge at least, mentioned fishing only in passing, but the two activities are essentially the same with different quarry and usually with different tools.
Hemingway was a world traveler, and much of his writing about hunting takes place in Africa. In his short stories and in The Green Hills of Africa he is often very precise about the specific gun calibers and bullets used. The locales of his fishing stories span from Michigan to Spain and to Cuba and are similarly detailed about equipment and technique. Faulkner focused on his home area in northwest Mississippi, and although very descriptive of the terrain and the hunt he gave only a general description of the gun, letting the reader know not much more than whether it was a rifle or shotgun.
Pursuit of fish or game heightens senses: sight, sound, and smell. In social situations, Faulkner quietly watched and listened. Hemingway was quoted as saying he disliked cigarette smoking because as a hunter he was sensitive to the disagreeable smell.
Hunting and fishing have not been necessities for most people in the world for some time, and those of us who are drawn to these activities often ponder what it is about them which entices us. This pondering leads some to questioning about humans' place in nature and how other human activities might reflect these very basic urges. For me, in very different ways both Hemingway's and Faulkner's writings display these questions.