If your back is hurting after doing a lot of crunches or situps, your are probably damaging you lower back.
But are they really that good for you?
When you isolate your abs by doing situp or crunches you are not going to burn any large amount of calories, so by them selves they are not a good fat loss option.
Then again, you’re not going build much muscle either, except maybe in your core.
That said, there are a lot of exercises that are better for core strength and conditioning than situps.
A simple Google search will allow you to find many exercises that are beneficial to your abs and, even exercises that develop strength and endurance.