This work demonstrates the influences of electrochemical reversibility of the pseudocapacitive materials on the performances of an asymmetric supercapacitor consisting of a pseudocapacitive cathode and an anode of the double-layer type. Thanks for the simple, one-step, cathodic deposition of nickel and cobalt hydroxide (denoted as Ni(OH)2 and Co(OH)2, respectively) films from their chloride precursor in aqueous media with the addition of 40 mM NO3 − as the OH-donating agent. The specific capacitances of Ni(OH)2 and Co(OH)2 films (ca. 0.4 mg cm−2) deposited at 1.0 mA cm−2 for 1000 s are equal to 2217 and 549 F g−1, respectively while the electrochemical reversibility of Co(OH)2 is better than that of Ni(OH)2 based on peak potential difference and symmetry of charge/discharge curves. The Co(OH)2-graphene asymmetric supercapacitor shows higher capacitance retention and higher energy efficiency of charge–discharge than the Ni(OH)2-graphene system although the latter system exhibits higher energy and power densities than the former one. The microstructures of as-deposited Ni(OH)2 and Co(OH)2 films have been examined by scanning electron microscopic (SEM), transmission electron microscopic (TEM), and X-ray diffraction (XRD) analyses.