Sulphur better than hydrogen
This article on Sabine Hossenfelder’s Youtube channel mentions a number of reversible chemical reactions which can be used to store energy. The advantage of a chemical reaction to store energy is that it should not be limited in time, there are no ‘leakage’ losses that there would be with heat, for example.
Of course, a battery is also a reversible chemical reaction, one which has the advantage of producing electricity directly as its output, rather than heat which has to be converted to electricity.
The main one she talks about is using solar energy to change sulphuric acid to sulphur, and then burning it to produce heat to generate, while recovering the sulphuric acid. One advantage of this is that the energy input is heat, which could be obtained directly from the sun using mirrors. Hydrogen on the other hand starts from an electric current, so it also needs a solar energy collection step to start with.
However, a big advantage is that hydrogen is a convenient fuel which can be moved around and converted to electricity directly in a fuel cell where it is needed. Transporting sulphur, burning it in your car to drive the engine and putting sulphuric acid out of the tailpipe is not very practical.
She mentions others at the end including iron/iron oxide.