Itaipu (or comparable impoundages such as Three Gorges) provide both
capacity, indicated as installed GWe of generating capability, a measure of
power, and
storage, indicated as GWH of
energy generation. These are equivalent to the capabilities of an automobile's
engine (power) and fuel tank (storage).
Hydroelectric projects also virtually always provide additional services such as flood control, irrigation water, recreation, and waterways management (ensuring water flows, etc.), which also account for design elements including scale, etc.
Pumped hydro should provide a sufficient level of both capacity and storage, though in general the storage requirements are far smaller than traditional hydroelectric dams aimed at generation. There are quite small pumped hydro facilities, the compensation being that water levels can rise or fall considerably, often many metres in a single day's storage/generation cycle.
Gravity is in general a weak force, but water is relatively massive, largely non-toxic, and can be utilised through large-scale pump-generator units (~800 MW per generator IIRC), which is a scale few other options can match. Again, on balance, pumped hydro is a good solution, there's just not enough of it to go around.
