Although substantial improvement in capacitance, energy densities, and discharge times has been achieved for redox supercapacitors over the last several years, important challenges remain. These include high series resistance which limits the ability to quickly discharge these devices, excessive heat generation, and the coupled thermoelastic strain field which tends to deform the device materials. High stability composites based upon conjugated polymers that wrap single-wall carbon nanotubes (SWNTs) provide a platform to develop materials that can broadly impact these issues. This work compares the performance of a new class of hybrid materials, polymer-wrapped SWNTs to established electroactive polymer-based anode and cathode material benchmarks of poly(3,4-propylenedioxythiophene) for the construction of supercapacitors. These polymer-wrapped SWNT composites exploit rigid, polyanionic poly(aryleneethynylene)s which provide unusual solubility and dispersion characteristics for carbon nanotubes in several solvents.