A cross-over in the interfacial strength, with increase in the separation rate, is observed between graphite-cis-1,4-polyisoprene and amorphous silica-cis-1,4-polyisoprene interfaces. Molecular dynamics simulations are used to compare the traction-separation characteristics of the two interfaces in the opening mode of separation at various separation rates and temperatures above the glass transition temperature of cis-1,4-polyisoprene. It was observed that various parameters governing the interface strength, such as strength modulus (ratio of peak traction to the separation at peak traction), peak traction, and the work of adhesion are higher for the silica substrated interface at very low separation rates. However, at higher rates, the graphite substrated interface showed higher values for the strength parameters. The reasons for this interface strength cross-over are explained using the potential energy, mobility, entanglement strength, tensile stiffness, and densities of the polymer over both substrates and the interface cohesive binding energy. Based on these observations, it is concluded that silica filled rubber nanocomposites are suitable for normal automobile tire applications; however, graphite fillers may be more suitable for resisting very large impact loads. © 2018 Author(s).