TFA says 75% round trip efficiency, compared to 85% for batteries.

While there is no leakage as such, the storage vessels might require continuous cooling, unless they are buried deep in the ground and they are very well insulated.

For great enough capacities, so that the costs of the turbo-generator and of the compressor become relatively small, the cost per stored kWh should become significantly lower than for batteries, especially when considering the far longer lifetime.

For small capacities, batteries are certainly preferable, but for very large capacities this should be a very good solution.