Based on the viscous shallow-water equations two model approaches one with a finite difference body-fitted coordinates and the other with a finite element representation are contrasted in order to determine their efficiency, accuracy and robustness. The pros and cons of finite differences on curvilinear coordinates and the different finite element models on unstructured triangular meshes are compared by calculating the solution characteristics of the boundary-value problem. Both schemes are applied to model the tidal dynamics of the Red Sea.