Ideally, the round trip efficiency of abiabatic CAES is 100%, as would be the ideal round trip efficiency of isothermal CAES.
What isothermal CAES (with heat storage) would require is a larger storage volume per unit of energy storage capacity, since less heat is generated during the ideal compression. That heat generation is not inefficiency, it's something you want!
Only if the heat is discarded and you reheat with fuel do you benefit from isothermal compression.