This work investigates the modelling accuracy of distinct Reynolds-Averaged Navier-Stokes (RANS) equations and Scale-Resolving Simulation (SRS) methods in the computation of the flow around a circular cylinder at Reynolds number 3900. The study examines the dependence of the modelling and numerical accuracies on the physical resolution (range of resolved scales) and turbulence closure, along with their consequences for the physics behind the results. Six mathematical models are evaluated through validation exercises: RANS supplemented with linear and non-linear turbulent viscosity closures, Delayed Detached-Eddy Simulation, Improved Delayed Detached-Eddy Simulation, eXtra Large-Eddy Simulation, and Partially-Averaged Navier-Stokes equations. The results confirm the ability of SRS models to significantly reduce the modelling error in comparison to linear RANS closures. Nonetheless, attaining an adequate numerical accuracy with SRS models is clearly more demanding than with RANS models. It is also shown that non-linear RANS models lead to smaller comparison errors than traditional linear closures. All results indicate that the modelling accuracy of a given mathematical model in simulation of the present flow is determined by its aptitude to represent the spatial development of the vortex-shedding coherent structure.