Based on the viscous shallow-water equations two model approaches one with a finite difference and the other with a finite element representation are contrasted in order to determine their efficiency, accuracy and robustness. The finite element model was created in two versions: one using explicit velocity and elevation and the other using semi-implicit Coriolis and pressure gradient terms and a semi implicit velocity scheme in the continuity equation. 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. Results of M2 and K1 - waves and their residual currents and a comparative analysis of efficiency are presented.