Let us begin our sit ups vs crunches comparison, with the difference in technique between the two. First let us see how you do a proper sit up. Firstly, lie on your back on the floor. Next, bend your knees in a 90 degrees angle and place your feet flat on the ground. Raise your arms straight and keep them parallel to the ground and pointing towards your feet. While your feet and butt are resting on the floor, slowly raise your torso off the ground and towards the thighs. You can come up as far as you can. Then go reverse through all the motions and fall back again, on the back. Do the whole thing as slowly as you can, without any jerky movements. This constitutes one sit up!

Now let us see how an abdominal crunch is done. The starting position is same as the sit up. Lie flat on your back, with knees bent in 90 degree angle and feet, flat on the floor. Place your hands, crossed over the chest or behind the neck. Do not exert force on the neck. Now curl your shoulders towards the pelvis, without lifting your lower back. Then return back to the starting position. This constitutes one crunch! The essential difference is that crunches restrict movement to shoulders and abdomen, without bringing the lower back in to play.

Sit Ups vs Crunches: Muscles
The next point of sit ups vs crunches comparison is the target muscles of the two exercises. Sit ups involve the hip flexor and abdominal muscles. Crunches only target the abdominal muscles including the ‘rectus abdominis‘.

Sit Ups vs Crunches: Calories Burnt
If you make a comparison between the two exercises, the sit ups burn more calories than the crunches, but they also create more strain on the back.

Sit Ups vs Crunches: Risk
Crunches are safe exercises which can be easily performed by anybody. However, sit ups have an inherent risk of spine injury, due to the strain it puts on the lower back, if this exercise is pursued aggressively without considering one’s capacity. Medical research on the dynamics of a sit up has shown that the abdominal muscles are involved only in the first 30 degrees raise of shoulders, off the ground. The rest of the strain is totally taken up by the hip flexor muscles. That is why, crunches are more recommended as safer exercises.

Source: Buzzle.com, Gray Pilgrim, "sit ups vs. crunches"