A facile method for preparing hierarchical carbon composites that contain activated carbon (AC), carbon nanospheres (CNSs), and carbon nanotubes (CNTs) for use as the electrode material in supercapacitors (SCs) was developed. The CNS/CNT network enabled the formation of three-dimensional conducting pathways within the highly porous AC matrix, effectively reducing the internal resistance of an SC electrode. The specific capacitance, cyclability, voltage window, temperature profile during charging/discharging, leakage current, gas evolution, and self-discharge of the fabricated SCs were systematically investigated and the optimal CNS/CNT ratio was determined. A 2.5 V floating aging test at 70 °C was performed on SCs made with various hierarchical carbon electrodes. Electrochemical impedance spectroscopy, postmortem electron microscopy, Raman spectroscopy, X-ray diffraction, and X-ray photoelectron spectroscopy analyses were conducted to examine the electrode aging behavior. A hierarchical carbon architecture with an appropriate AC/CNS/CNT constituent ratio could significantly improve charge-discharge performance, increase cell reliability, and decrease the aging-related degradation rate.