In this work, we present a comparative study of the impact of secondary carbon nanofillers on the electrical and thermal conductivity, thermal stability, and mechanical properties of hybrid conductive polymer composites (CPC) based on high loadings of synthetic graphite and epoxy resin. Two different carbon nanofillers were chosen for the investigation—low-cost multi-layered graphene nanoplatelets (GN) and carbon black (CB), which were aimed at improving the overall performance of composites. The samples were obtained by a simple, inexpensive, and effective compression molding technique, and were investigated by the means of, i.a., scanning electron microscopy, Raman spectroscopy, electrical conductivity measurements, laser flash analysis, and thermogravimetry. The tests performed revealed that, due to the exceptional electronic transport properties of GN, its relatively low specific surface area, good aspect ratio, and nanometric sizes of particles, a notable improvement in the overall characteristics of the composites (best results for 4 wt % of GN; σ = 266.7 S cm−1; λ = 40.6 W mK−1; fl. strength = 40.1 MPa). In turn, the addition of CB resulted in a limited improvement in mechanical properties, and a deterioration in electrical and thermal properties, mainly due to the too high specific surface area of this nanofiller. The results obtained were compared with US Department of Energy recommendations regarding properties of materials for bipolar plates in fuel cells. As shown, the materials developed significantly exceed the recommended values of the majority of the most important parameters, indicating high potential application of the composites obtained.