The key to this is the moment of inertia.
The moment of inertia of the solid disk flywheel (ignoring the flange in the
middle) is given by:
I = 1/2 Mr2
The second flywheel can, to a first
approximation, be considered as a cylinder of mean radius,
The moment of inertia is given by:
I = Mr2
Therefore the second flywheel will
have a moment of inertia that is double that of the first. Therefore it
will store double the kinetic energy for any given angular velocity.