As far as my knowledge goes, Geochemical Cycle deals with the movement of elements within the five different components of the earth, while the Geological Cycle deals with the complex interactions between the component sub-cycles of tectonic, hydrologic, rock, and the biological cycling, wherein, these various subcycles influence each other and may produce natural hazards and processes important to environmental geology such as landslides, earthquakes, volcanic activity, flooding, groundwater flow, and weather.
In my opinion, generalizing the answer of Haider, to answer to this interesting, and fundamental, question, we should introduce the concepts of spatial and time scales which are characteristic of the geological cycles and sub cycles. In fact geological cycles involve, at different spatial-time scales, several geochemical processes, as far as geophysical in rheological sense and biological. In particular we could distinguish between micro, meso and macroscales where different contributions of the geochemical, geophysical and biological processes become relevant with different degrees and then they could exibit, in their cycles, different similarity with the geological cycles and subcycles intented as the all. Foundamentally it is a question of the scale similarity model.