Several technological routes are being investigated for improving the energy storage capability and power delivery of electrochemical capacitors. In this work, ternary hybrid electrodes composed of conducting graphene/reduced graphene oxide (rGO), which store charge mainly through electric double-layer mechanisms, covered by NiO nanostructures, for adding pseudocapacitance, were fabricated through a matrix assisted pulsed laser evaporation technique. The incorporation of multiwall carbon nanotubes (MWCNTs) provokes an increase of the porosity and thus, a substantial enhancement of the electrodes' capacitance (from 4 to 20 F cm-3 at 10 mV s-1). Volumetric capacitances of 34 F cm-3 were also obtained with electrodes containing just carbon nanotubes coated with NiO nanostructures. Moreover, the use of nitrogen containing precursors (ammonia, urea) for laser-induced N-doping of the nanocarbons also provokes a notable increase of the capacitance. Remarkably, N-containing groups in rGO-MWCNTs mainly add electric double layer charge storage, pointing to an increase of electrode porosity, whereas redox reactions contribute with a minor diffusion fraction. It was also observed that the loading of carbon nanotubes leads to an increase of diffusion-controlled charge storage mechanisms versus capacitive ones in rGO-based electrodes, the opposite effect being observed in graphene electrodes.