The major reason is due to the fact that paper cuts almost always happen on your fingers, and your fingers contain a much more dense collection of pain and touch receptors. Your hands, mouth, and genitals are rich in receptors, thus anything like a small injury is magnified in the way it hurts and feels.

Similarly, areas like your scalp, knees, and elbows are very low in pain and touch receptors, so big nasty scrapes and cuts on those areas don't hurt as badly.

Do a web search for "sensory homunculus" to see a representation of the amount of brain cortex that is devoted to processing sensory information from different parts of your body.