You'll get a good idea on the differences by comparing these two pages side-by-side: exrx.net/WeightExercises/RectusAbdominis/B
You'll notice that sit ups are basic exercises that involve a lot more synergist muscles than basic crunch. It's possible that the difficulty in performing a sit-up may be caused by one or more of those synergists not being strong enough.
If your reason for doing either exercise is just to target abs, then crunch is good enough to start with. It is also a good starting point to create a decent amount of ab strength to help doing sit-ups correctly (see: exrx.net/Questions/DangerousExercises.html
At later stages once you get comfortable with your own strength, variety is the key and you really should experiment on a whole plethora of different exercises per each muscle group.