The optimal strategy to numerically solve the Richards equation is problem-dependent, especially on GPUs because an efficient numerical scheme on CPU might not scale well on GPU. In this work, four numerical schemes are coded to investigate their parallel performance on CPU and GPU. The results indicate that the scaling of Richards solvers on GPU is affected by the numerical scheme, the linear system solver, the soil constitutive model, the code structure, the problem size and the adaptive time stepping strategies. Compared with CPU, parallel simulations on GPU exhibit stronger variance in the scaling of different code sections. The poorly-scaled components could deteriorate the overall scaling. Under all circumstances, using a GPU significantly enhances computational speed, especially for large problems. Clearly, GPU computing have significant potential in accelerating large-scale hydrological simulations, but care must be taken on the design and implementation of the model structure.