These two categories of presentation are so broad and fundamental that in the famous words of Niels Bohr, “The opposite of a trivial truth is false; the opposite of a great truth is also true.”
In William Jackson’s answer, he points out that energy is synonymous with ‘force displacement’ and matter is definable as ‘force duration’. In the terms that I am using here, his definition associates energy with space or length (dis-place-ment) and matter with time (duration), both of which are modes of the same underlying force-field. This ultimately characterizes displacement as an active force and duration as a passive field, which I agree with, however, it conflates energy and matter with the job that they are doing rather than what they are; who or what is causing these effects.
I propose a different conjecture on the root nature of matter and energy. In a way contradicting the previous explanation, matter would be more like length or lengthening of energy through time, and energy would be analogous to directly felt or experienced motivation to oscillate or wave. While we are used to understanding the passage of time as the measurement of the progress of the hand of a clock around the dial, all clocking instruments (chronometers) are based on the uniform oscillation of a physical substance.
To measure time or express the passage of time, something must experience it directly. To express time or energy in matter, the best that we can to is to infer it with arrows or wavy lines, recursive Cubist geometries, etc. It has to be inferred metaphorically to an audience which can make sense of this as an experience of change or sequence.
In the simple physics-friendly terms then, I propose that matter is length and energy is oscillation. Another way of saying it is that
energy is the presence which is wound up within the ‘private figurative depths’ of matter, and
matter is how those depths represent their interactions to each other (i.e. public-facing literal surfaces) at any given moment.
Energy is the who, the why, and the when of the cosmos; matter is the what, the how, and the where.
Energy is the impetus for sequences of time, and matter is the reflected consequence, the entropic-gravitational falling back of energy’s ‘spring forward’.