In a compost bin, air-breathing microorganisms break down your waste and create heat. A compost bin can handle more food scraps than a worm farm. You will need an outdoor space and garden cuttings to mix in with your food scraps.
The worms in worm farms break down your food scraps by eating the microorganisms that eat your food. Worm farms work well for apartments and children love them. Worm farms need a very sheltered location and cannot process as much material as a compost bin. The variety of material you can put in a worm farm is also more limited than with a compost bin.