The symmetric supercapacitors (SC) are electrochemical capacitors with higher energy density than conventional ones. Both their positive and negative electrodes contain the same type of electrode active material. Carbon xerogels are a kind of carbon material which properties can be designed, structurally and chemically, in order to fit the requirements for their final application. They possess tunable porosity, high purity, and electrical conductivity and are very relevant for their use as active material for electrodes in supercapacitors. In this study, the electrochemical properties of symmetric supercapacitors were compared by using a polymer Aquivion™ electrolyte membrane (as electrolyte and separator) and the common aqueous electrolyte (i.e., 1 M KOH). The membrane was previously exchanged to the K+-form by immersion in 1 M KOH. The electrode active material was an activated carbon xerogel (AX-1500) prepared by polymerization of resorcinol and formaldehyde in a sol–gel microwave-assisted process. Electrochemical tests were carried out by cyclic voltammetry, galvanostatic charge/discharge measurements, impedance analysis, and long-term durability tests. The relationship between the structure and morphology of the carbon xerogel and the nature of the electrolyte was established, which may be relevant for the design of supercapacitors providing high power and energy densities.