The fundamental property is: a time constant in the seconds range.

Electrolytics are in the milliseconds to tens of microseconds range, and batteries are in the minutes to hours range.

What is the meaning of this time constant? It is the fastest you can discharge the device. It is also a measure of how fast you can draw some load at some efficiency. The short circuit current is the most current you can possibly draw; and a short circuit does zero work, so the efficiency is zero. A half-short dissipates half the energy, so has an efficiency of 50%, and takes twice as long to discharge. It follows: lower currents, applied for longer time scales, can be drawn at higher efficiency.

Eventually, as time scale goes up, efficiency goes back down, as self-discharge begins to dominate. Usually a time constant of weeks or months.

This generalizes to all energy storage media: there is a minimum and maximum rate at which that energy can be cycled, at a given efficiency. In this way, you can determine which type of device is desirable for a given application.

Tim