An express method for assessing the effectiveness of lubricating compositions with nano-additives of various chemical compositions is proposed, and a joint analysis of experimental data on the changes in the value of wear and the level of damage to the surface layers of metallic friction pairs was performed. The variation in the current relative hardness of the sample’s surface, the variation in the current relative material damage level, the current value of wear, and the current level of the coefficient of friction were chosen as the key parameters to conduct a performance assessment. The level of material damage in the contact zone was determined using the parameters of the statistical law of hardness value scattering. Based on an analysis of data in the literature, it was observed that the structural changes occurring in metallic materials during long-term, cyclic, static, and frictional loading are correlated with changes in the statistical characteristics of the hardness scattering results. An experimental substantiation of the proposed method was carried out for steel-sliding friction pairs using lubricating compositions based on Greaseline Lithium BIO Rail 000 oil manufactured by AIMOL with nano-additives of copper, magnesium and aluminum alloys, graphite, and two grades of medium-carbon steel. According to the system of indicators presented in this research, the greatest efficiency (in terms of increasing the wear resistance of friction steel pairs) was achieved with lubricating compositions including nano-powder additives made of steel, which have lower hardness. For the friction experiments, where the determining factor was abrasive wear, such lubricants ensured minimal damage and wear to the friction surface, while the value of the friction coefficient was maintained at a level that is optimal for wheel–rail friction pairs.