Compared to carbon nanotubes (CNTs), graphene possesses high strength due to wrinkled surface texture caused by a high density of surface defects which benefits more contact with the polymer material than a rolled-up CNT. In the present review, we have discussed and compared the various properties of CNTs (1-D) and graphene (2-D) obtained in experimental results. The effects of covalent and non-covalent functionalization of CNTs and graphene on the properties of its composites have also been reviewed and compared. A comparative analysis has been carried out between CNTs and graphene-reinforced polymer composites. Furthermore, the synergetic effects of CNTs and graphene hybrid nanofiller on the mechanical properties of polymer composites have also been briefly discussed. Finally, this review concludes with the potential application and future challenges are discussed with regards to filler and their polymer composites.