the energy of matter implies the movement of masses, and wave energy has no moving masses
The energy of particles (matter) is the ability to do some work, so the energy can be movement in the form of kinetic energy or in the configuration of a system called potential energy, the sum of these two energies is constant.
A wave is formed as a result of perturbation of the medium by a substance, therefore, for the formation of a wave, a substance supplies energy, for example: in the form of motion, in the form of an electric or magnetic field oscillation, etc.
Waves after formation can move away from the substance that formed them, transferring energy that alternately has kinetic and potential energy, but the total energy is constant.
Therefore, the energy in matter is caused by the movement of the same, and the energy in the wave does not require the movement of matter, so this is a more efficient way of doing the work.
In conclusion, the energy of matter implies the movement of masses, and wave energy has no moving masses.