This study presents electrospun niobium carbide/carbon (NbC/C) hybrid nanofibers, with an average diameter of 69 +/- 30 nm, as a facile precursor to derive either highly nanoporous niobium carbide-derived carbon (NbC-CDC) fibers for supercapacitor applications or niobium pentoxide/carbon (Nb2O5/C) hybrid fibers for battery-like energy storage. In all cases, the electrodes consist of binder-free and free-standing nanofiber mats that can be used without further conductive additives. Chlorine gas treatment conformally transforms NbC nanofiber mats into NbC-CDC fibers with a specific surface area of 1508 m2 g-1. These nanofibers show a maximum specific energy of 19.5 W h kg-1 at low power and 7.6 W h kg-1 at a high specific power of 30 kW kg-1 in an organic electrolyte. CO2 treatment transforms NbC into T-Nb2O5/C hybrid nanofiber mats that provide a maximum capacity of 156 mA h g-1. The presence of graphitic carbon in the hybrid nanofibers enabled high power handling, maintaining 50% of the initial energy storage capacity at a high rate of 10 A g-1 (64 C-rate). When benchmarked for an asymmetric full-cell, a maximum specific energy of 86 W h kg-1 was obtained. The high specific power for both systems, NbC-CDC and T-Nb2O5/C, resulted from the excellent charge propagation in the continuous nanofiber network and the high graphitization of the carbon structure.