A good carbon frame can be laterally stiff and vertically compliant, something that is hard to accomplish on metal frames with traditional tubes.
The stereotype is that cheap aluminum is stiff, cheap steel is heavy, and cheap carbon is stiff and rides like wood. Compliant aluminum, light steel, and compliant carbon exist but one must pay for the additional engineering and manufacturing steps.
Many companies offer different carbon frames ranging in verticle compliance for different types of riders and rides.