Case, and Deere go head to head in almost every market. New Holland and a couple others also play in the same markets depending on what KIND of machine you're looking to run. Tillage tractors are pretty much fendt/challenger, NH, deere, case. When you get into combines/coppers other brands also play. For the consumer and/or smaller tractor market there's all sorts of options.
Why people go deere or case is simple. It's the supply chains. You have N days to get your crop in the ground, and Y days to get your crop harvested. Deere and case have the best(and most expensive) field techs and dealer support. "A machine is only as good as your dealer support" is the phase almost everyone uses when shopping for equipment. Anyone with a significant investment of tractors(non-hobby farmers) can have a case or deere tech replace or fix damn near anything in hours or days, on site.