The micro-scale analysis of frictional contact with large sliding is important for understanding the tribological behaviour arising in engineering surfaces, particularly for predicting the apparent coefficient of friction. Numerical simulation of micro-scale contact between rough surfaces can be used to gain a deeper understanding of the phenomena involved. The boundary condition associated with compression can be modelled during the sliding by prescribing the normal force or by prescribing the normal displacement. Therefore, a comparison of these two assumptions is presented and discussed for the contact between a flat rectangular deformable body and a sinusoidal rigid rough surface. The deformable body, modelled withing a representative contact element (RCE), is assumed elastic-perfectly plastic and it is discretized with a non-conforming mesh of 8-node hexahedral solids elements. Different contact conditions were simulated: (i) different values of friction coefficient; (ii) different values of initial normal compression stress; (iii) different values of wavelength in the definition of the rigid surface roughness. The influence of assuming a load control or displacement control was assessed for these conditions. The results reveal two main differences. First, the ratio between the apparent and real contact areas is generally more stable during sliding when displacement control is adopted, allowing steady state to be reached with a shorter sliding distance. The only exceptions occur for low normal loads (25% of the material yield strength). Second, displacement control also leads to a more stable apparent coefficient of friction, defined as the ratio between the total tangential and normal forces, throughout sliding. In contrast, both approaches exhibit similar trends, including a direct proportional relationship between the real contact area, the Coulomb friction coefficient and the applied normal load.