The abdominal crunch is a popular exercise, effectively targeting the abdominals (rectus abdominis), as well as the oblique muscles which run down the side of the abdomen. Whilst the crunch is performed with a much smaller range of motion compared to that of the sit-up, it is the abdominals which are specifically responsible for the flexion of the lumber and thus isolated during the crunch, whereas the sit-up involves the hip flexor muscles to a great degree which somewhat negates the abdominal stimulus.
For those looking to reduce fat around the stomach and hips, the crunch is a great exercise for developing the abdominal muscles, but will not lead to specific fat reduction from the region. Instead, the best approach is to follow a training program and diet which will lead to overall fat loss. You will notice the development of the abdominals to a much greater degree once fat levels decline, leaving you with a much firmer and defined midsection.