Vegetation affects the mean and turbulent flow structure in surface water bodies, thus impacting the local transport processes of contaminants and sediments. The present paper explores the capability of two different mathematical models to predict fully developed one-dimensional open channel flow in the presence of rigid, complex-shaped vegetation with leaves, submerged or emergent. The flow is described by applying two different turbulence closure schemes, both of which are based on the Boussinesq eddy viscosity model: a suitably modified $kappa$ - $varepsilon$ model and a two-layer model based on the mixing length approach. To describe the turbulence structure within and above the canopy a turbulent kinetic energy budget equation was added to the two-layer model. The results of the models were compared with experimental data where simple cylinders, plastic plant prototypes, or real plants, all arranged in a scattered pattern, were employed. Since good agreement between the results of the models and measurements was found in comparing velocity and turbulent shear stress, the models could potentially be used to assess vegetative resistance. Significant disagreement was found when comparing measured and computed eddy viscosity distributions, streamwise turbulence intensity, and most of the terms comprising the turbulent kinetic energy budget.