According to Bodybuilding.com, crunches are preferable for those wishing to work their abdominal muscles and get them in shape. Sit-ups rely primarily on the psoas muscle that runs from the lower back to the front of the thighs; as a result, they do little to build the abs.
The sit-up also relies on muscles in the chest, the hips, the lower back, the neck and, if the feet are hooked, the lower legs. It is, therefore, not a recommended exercise for anyone with back, hip or neck problems. When doing a crunch properly, only the head and shoulders are raised from the floor when the abdominal muscles contract. Any attempt to pull the head forward only serves to activate other muscles and detracts from the value of the crunch.