Carbon nanomaterials secure promises of incorporating exceptional mechanical performance and multifunctional properties into polymers. However, questions concerning type of carbon nanofiller, fraction and corresponding change in relevant property are yet to be answered. In this study, graphene platelets (GnPs) and carbon nanotubes (CNTs) were added individually into epoxy adhesive and corresponding structure-property relations were investigated experimentally and numerically. The study shows that: at fractions  0.25 vol%. The mechanical performance of the single lap joint specimens with different nanocomposite adhesive were further investigated using 3D finite element analysis. The numerical analysis not only confirms the outcomes of the experiments but also shows that the failures in the nanocomposite adhesive layers occurred due to Mode II failure. Electrical conductivity measurements of epoxy nanocomposite adhesives showed lower percolation threshold (0.54 vol%) for epoxy/CNT nanocomposite adhesive compared to 0.63 vol% when GnPs were used. The contrast in the geometrical structure between GnP (plate-like structure) and CNT (tube-like structure) is crucially responsible for epoxy nanocomposite adhesives’ properties. This research pointed out that selecting a carbon filler for a polymer composite is key-factor to determine the end-product function.