It should be noted that the energy stored in the pressure of gas is zero. All the energy of an ideal gas is the kinetic energy (and rotational/vibrational energy) of its molecules, which is thermal energy. Internal energy of an ideal gas is independent of pressure.

What compressed gas storage does is (aside from combustion energy of a fuel gas) to provide not a store of energy, but a store of reduced entropy, enabling otherwise unusable amounts of heat to be converted to work.