A detailed numerical study of the flows around the airfoil NACA 23012 near stall, at angles-of-attack ranging between 12.4° and 16.2°, Mach number M = 0.18 and Reynolds number Re = 1.8 million, was conducted by Reynolds-averaged Navier–Stokes (RANS) equations closed by the commonly employed Menter’s k–ω shear stress transport (SST) turbulence model in contrast to the wall-modelled large eddy simulation (WMLES). All these flow simulations were performed in ANSYS FLUENT on the same, sufficiently refined computational mesh with dimensionless wall distance y + ≈ 30. The comparison of the obtained numerical and available experimental results points to the inability of RANS modeling to adequately capture the flow in the post-stall region whereas it performs satisfactorily in the attached, pre-stall region. Although relative errors of lift and drag coefficients remain within an acceptable range, the numerical stall seems delayed or not predicted at all. On the other hand, WMLES manages to reproduce the expected trend of aerodynamic coefficients, while the actual numerical values appear underrated in comparison to the measured values. Both modeling approaches are critically evaluated with regard to the flow separation phenomenon appearing at airfoils at high angles-of-attack and some conclusions are provided.