The aim of this paper is to systematically compare k-epsilon and Mellor-Yamada two-equation turbulence models. Both models include prognostic equations for turbulent kinetic energy and a length scale related parameter which are used to calculate eddy viscosities and vertical diffusivities. The results from laboratory experiments, using mixed and stratified flows, are simulated in order to systematically compare and calibrate the models. It is shown that the Monin-Obukhov similarity theory is well represented in both models. The models are used to simulate stratified tidal flow in the Irish Sea, and the results show that the k-epsilon models generally predict a larger phase lag between currents and turbulent dissipation, in the bottom boundary layer, than the Mellor-Yamada models. The comparison between the model results and field measurements, of the rate of dissipation of turbulent kinetic energy, shows that both models require modification through the inclusion of an internal wave parameterization in order that they are able to correctly predict the observed levels of turbulent dissipation. As the main result, it is shown that the choice of the stability functions, which are used as proportionality factors for calculating the eddy viscosity and diffusivity, has a stronger influence on the performance of the turbulence model than does the choice of length scale related equation.