The role of subgrid scale (SGS) viscosity is investigated in LES and VMS-LES simulations of the flow around a circular cylinder at Re=20000 on unstructured grids. The separation between the largest and the smallest resolved scales in the VMS formulation is obtained through a variational projection operator and finite-volume cell agglomeration. Two different non-dynamic eddy-viscosity SGS models are used both in classical LES and in VMS-LES. The sensitivity of the results to different parameters, such as the value of the SGS model input coefficient or the agglomeration level and to numerical viscosity in VMS-LES, is also addressed. Finally, a possible indicator of quality of the LES and VMS-LES predictions is examined.