Carbide-derived carbon (CDC) aerogels with hierarchical porosity are prepared from cross-linked polycarbosilane aerogels by pyrolysis and chlorine treatment at 700 and 1000 °C. The low-temperature sample is further activated with carbon dioxide to introduce additional micropores. The influence of the micropore structures resulting from the different synthesis conditions and the effect of the combination of high specific surface areas of more than 2400 m²/g with the aerogel-type texture on the electrochemical properties of the carbons are investigated. Electrical double-layer capacitors (EDLCs) are assembled with 1 M aqueous (H₂SO₄, Li₂SO₄, LiCl, HCl), organic (1 M tetraethylammoniumtetrafluoroborate in acetonitrile), and ionic liquid (1-ethyl-3-methylimidazoliumtetrafluoroborate) electrolytes. The larger micropores and higher surface area of the CDC aerogel prepared at 700 °C lead to higher capacitance compared to the material prepared at 1000 °C. Carbon dioxide activation leads to extremely high capacitance retentions at high current densities up to 60 A/g, which is critical for high power applications. High gravimetric specific capacitances with stable cycling and high capacitance retentions are achieved in all the studied electrolytes. This renders CDC aerogels versatile electrode materials for EDLCs with various electrolytes.