What are the similarities and differences between the water and carbon cycles?

Difference: Carbon cycle requires life, and the water cycle just requires sunlight. So former would continue to occur without life, but the latter would not. 

Similarity: They both use Plants as an Integral component. The water cycle uses plants for uptake of water and transpiration from the surface whereas carbon is used in photosynthesis and also form the body of the plant (through various organic molecules)

Hope this helps!