A good example of this would be a squat. Most people do a basic (or half) squat. This is when your heels stay on the floor and your knees do not go past your toes. The full squat is much harder because of the pressure on the knees and the importance of hip flexor flexibility.
When you start exercising it's always recommended that you perform half squats until body awareness improves and you're better conditioned for the exercise.
The sit-up is the same kind of thing. Sit ups have a bad reputation for being bad on the back, causing problems ranging from numbness to spinal damage. However, it's the sit-up you see athletes and the military performing. So whats the deal?
A full sit-up also requires hip flexor flexibility and requires a more perfected technique. When you do a sit-up, you need to lift your body off the floor in a very controlled motion, first with your upper and then lower spine.
Sit-ups can be risky for a beginner or for a personal trainer who responsible for a client's safety.
A crunch on the other hand is almost foolproof. You can do a crunch wrong and for the most part. it's just ineffective. The only thing you need to know about crunches, is that you shouldn't place your hands behind your head and push on your neck while raising to the crunch position.
A crunch doesn't work hip flexors as well as a sit-up, but I assume most exercisers are doing crunches and sit ups to strengthen their abs anyway. I can't say I've ever heard (in my entire career) a client say "I want to develop crazy strong/defined/muscular hip flexors!"
For training the abdominal region, crunches are just as effective as a sit up. The abs are worked during the first 30 degrees of the sit up and the hip flexors for the remaining 70. A crunch is just working the abs, and that's perfectly okay. You can work on hip flexor strength and flexibility during lower body training routines.
I think this is a case, where it's better to play it safe. I have hearing been hearing that sit-ups are dangerous for a long time and it can't be for no reason. Even the U.S. Armed Forces have eliminated sit-ups from their training program.
There are so many crunch variations, so get the most of them and if you still want to try sit ups, start very small (like 10-20 sit ups) and monitor how you feel at every step. During and after the exercise.
Play It Safe!