Dynamic multimedia fate models (MFMs) have to deal with the temporal and spatial variation of physical-chemical properties, environmental scenarios, and chemical emissions. In such complex simulation tools, an analytical solution is not practically feasible, and even a numerical approach requires a suitable choice of the method in order to obtain satisfying speed and reliability, particularly when certain combinations of modeling scenarios and chemical properties occur. In this paper, considering some examples of a wide range of realistic chemical and scenario properties, some sources of stiffness in MFM equations are pinpointed. Next, a comparison of the performances of several numerical schemes (chosen as representatives of three wide classes) is performed. The accuracy and the computational effort required by each method is evaluated, illustrating the general effectiveness of automatically adapted timesteps in numerical algorithms and the pros and cons of implicit timestepping. The results show that automatic error control methods can significantly improve the quality of the computed solutions and most often lead to relevant savings in computing time. Additionally, explicit and implicit methods are compared, indicating that an implicit method of medium order (around 5) is the best choice as a general purpose MFM computing engine.