Lightsail Energy tried and failed to bring this to market - not sure whether this can ultimately outperform Lithium Ion Batteries, which have all the pressure of the electronics industry behind them.
I feel like they have different applications so they're not necessarily competing. Obviously compressed air systems will never have the energy density of a battery, but they could be much more reliable. It also scales up really easily, and I think that's where the sweet spot is - I've heard of people sealing off caves to make giant air storage tanks for these projects.
The charge/discharge efficiency for compressed air is terrible since most of the energy gets wasted as heat. This plus the terrible volumetric energy storage density makes it a nonstarter for most applications.