Beyond the benefits of buying less expensive cuts of meat, slow cooking will help you feed more for less. It's no accident that dishes like soup and stew can feed a crowd with few ingredients. Hearty peasant food is filling, wholesome, and lets you stretch what you have because you're adding water to the mix and letting the natural flavors of the ingredients permeate the liquid. That lowly potato, carrot or turnip won't taste like a mere root vegetable when you're done. It will be part of a blended meal that, instead of feeding four, will easily serve five or six because of the addition of less expensive ingredients, water and a few spices.
Slow cooking saves energy, too. You won't be firing up the oven to cook, and that's good for your wallet and the environment.