The efficiency of any storage is an important factor. The efficiency is the the ratio of the energy sored to the energy recovered. The efficieny of CAES and also adiabatic CAES is poor even if the heat is stored. The reason is the high temperature the process is run. High temperature in an expansion leads to high power, however the efficiency is low due to simple thermodynamic reasons. This is illustrated in the presentation below:
Whereas the efficiency of any other CAES process is smaller than 40 % the efficieny of the erneo process is 85% and higher.