The electrical conductivity and percolation onset of graphene-based nanocomposites are studied by varying both planar and transversal aspect ratios of graphene nanoplatelets (GNP) fillers using a three-dimensional stochastic percolation-based model. The graphene nanoplatelets are modeled as elliptical fillers to enable planar aspect ratio variations. We find that decreasing the graphite’s thickness results in an exponential performance improvement of the nanocomposites, in contrast to a linear improvement obtained when the planar aspect ratio is increased, for the same filler volume. Furthermore, we show that hybrid nanocomposites fabricated with partial replacement of GNP by carbon nanotube (CNT) may improve the electrical performance of the GNP monofiller composites. Improvement or deterioration of the electrical properties is mainly based on the morphology and content of the fillers mixed in the hybrids. Nonetheless, using a minimal amount of CNT for substitution always leads to the highest improvement in conductivity in the hybrids, while additional CNTs only lead to smaller improvement at best or even deterioration. The results are validated against experimental works and offer useful insights for the fabrication of highly conductive nanocomposites.