The accurate prediction of fluid flow within rotating systems has a primary role for the reliability and performance of gas turbine engine. The selection of a suitable model to account for the effects of turbulence on such complex flows remains an open issue in the literature. This paper reports a numerical benchmark of RANS, DES and LES approaches available within the commercial CFD solvers Star CCM+ and CFX together with results obtained by means of in-house developed or opensource available research codes exploiting an innovative Reynolds Stress Model closure, a direct numerical simulation and additional RANS and LES models. The predictions are compared to experimental data available in the literature for two test cases. Test case 1 corresponds to a closed Taylor-Couette cavity with endcap rings, considered experimentally by Burin et al. Test case 2 corresponds to a Taylor-Couette system with an axial Poiseuille flow studied experimentally by Escudier and Gouldson. The results are compared and discussed in details for both the mean and turbulent fields. Most of the approaches predict quite well the trends apart from the SST models, which provide relatively poor agreement with the experiments. Even though no approach appears to be fully satisfactory, the innovative RSM closure offers the best overall agreement in both closed and opened Taylor-Couette cavities.