Power-density and energy-density.
The "secret" to dense flywheel energy storage is in the equation: Energy = 1/2 * I * w^2
Where "w" is rotational speed in radians/sec, and I is rotational-inertia / rotational-mass. So you store the most energy by rotating it as fast as possible. 20,000 RPM stores 4x the energy of 10,000 RPM.
The issue with water, or really... anything outside of steel and other such incredibly strong materials... is that water doesn't hold itself together very well. As such, the RPM limit would be smaller than a steel-flywheel.
Indeed, steel is still not used in advanced flywheels, because some forms of plastic IIRC are superior at the kinds of stresses we're talking about. Thus, these plastic / composite material flywheels, while much lighter, can spin much faster.
Leading to more efficient energy storage.
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In effect, you need every part of the flywheel designed to hold itself together to reach maximum efficiency. Water is the exact opposite. Its a lot of mass but basically no ability to handle stresses. Solid Steel would be better and would spin faster.