This study provides a detailed comparison of two turbulence closures for aerodynamic flows around high-lift airfoils; the first based on turbulent viscosity and the second on the algebraic Reynolds-stress approximation. A detailed analysis of their derivation helps shed light on their inherent limitations in predicting complex flow phenomena such as confluent boundary layers and flow separation found in typical take-off and landing conditions.One of each of the following categories: one-equation, two-equation, IARSM and EARSM is selected and compared on several low-speed high-lift configurations. Comparisons to experimental data for both mean flow and turbulence quantities are provided for all cases studied.Amongst the turbulent viscosity models coded and studied are the Spalart-Allmaras, Baldwin-Barth, Wilcox k - o and Menter's Shear Stress Transport model. A parameter study based on different pressure-strain correlations and dissipation models (or near-wall treatment) is included when studying the algebraic Reynolds-stress models for both the explicit (EARSM) and the more traditional or implicit (IARSM) forms.Results are generally very promising and of sufficient accuracy for engineering interest. Overall, the study indicates that for flows around low-speed high-lift airfoils, the algebraic Reynolds-stress construct does not represent a higher level of description than the eddy viscosity models since it fails to improve on accuracy. The basic underlying assumption of weak-equilibrium in algebraic Reynolds-stress models is outperformed by well calibrated eddy-viscosity models.