Understanding of wear behavior in dual-side graphene coatings is essential for the reliable design of nanomechanical systems. In this study, molecular dynamics simulations are employed to investigate the effect of surface roughness (SR) matching on the nanoscale wear response of dual-side graphene-coated interfaces. Key parameters, including critical wear load, peak friction force, stress distribution, and graphene bending angle, are systematically evaluated under both matched and mismatched SR conditions. The results reveal a correlation between roughness compatibility and nanowear performance. Specifically, SR matching leads to balanced stress distribution and comparable critical wear loads on both contacting surfaces, resulting in more uniform and predictable wear behavior. In contrast, mismatched SR conditions cause stress asymmetry and localized deformation, making the graphene layer on the rougher surface more prone to damage. These findings enhance the understanding of nanowear mechanisms in graphene-based coatings and offer a quantitative basis for optimizing their durability and performance in advanced engineering applications.