i think it's the amount of effort you put into the action - sit-ups can be quite gentle, crunches are the butch way of doing it. When ever I get the urge to do either, I lie down and wait until it passes off!
Sit ups basically involve the use of uper body where as crunches involve the legs also. People tend to suggest that you no longer do sit ups as it puts too much strain on the body.
sit ups, done with the legs straight, are assisted by the muscles in the leg. It is for this reason that most people will now do crunches, with the legs bent and feet flat on the floor, as this isolates the abdominal muscles... so not only are they more effective at developing your actionman-esque six pack they are also less risky for your back and neck if you are prone to injury or are just starting out.