Conductive natural rubber (NR) nanocomposites were prepared by solvent-casting suspensions of reduced graphene oxide (rGO) or carbon nanotubes (CNTs), followed by vulcanization of the rubber composites. Both rGO and CNT were compatible as fillers in the NR as well as having sufficient intrinsic electrical conductivity for functional applications. Physical (thermal) and chemical reduction of GO were investigated, and the results of the reductions were monitored by X-ray photoelectron spectroscopy for establishing a reduction protocol that was useful for the rGO nanocomposite preparation. Field-emission scanning electron microscopy showed that both nanofillers were adequately dispersed in the main NR phase. The CNT composite displays a marked mechanical hysteresis and higher elongation at break, in comparison to the rGO composites for an equal fraction of the carbon phase. Moreover, the composite conductivity was always ca. 3-4 orders of magnitude higher for the CNT composite than for the rGO composites, the former reaching a maximum conductivity of ca. 10.5 S/m, which was explained by the more favorable geometry of the CNT versus the rGO sheets. For low current density applications though, both composites achieved the necessary percolation and showed the electrical conductivity needed for being applied as flexible conductors for a light-emitting diode.