The penetration depth in tissues or generally matter ultimately depends on processes (reflection, absorption, scattering, photochemistry) which might or may not occurs depending on composition and microscopical features.
Basically, rather than energy alone, you can think of the corresponding frequency of the em radiation (E = hf for a photon, where f is the frequency of the wave emerging from an ensemble of such photons and h the Planck's constant).
All the processes I've just mentioned require a tuning (or some offset for scattering) of this frequency, like a radio stay tune to a particular channel.
So don't assume that a photon of higher frequency (higher energy) does more then a less energetic one. There might not be a process ready for it, or the occurrence of an event might require a longer transit thus resulting in a high penetration depth.
From the above it should also be clear that penetration depth does not monotonically depend on the energy. As you said, microwaves can penetrate biological tissues. But much more energetic x-rays can do it too. Somehow in the middle are UV and Vis radiation, which are quite effectively blocked by reflection, absorption (melanin pigment in case of our skin) and even scattering. For the last, you can illuminate with a "white" light your finger, and see that red light propagates most, similar to the Rayleigh diffusion giving red sunrises and sunsets.
(For the other question "why MW are less energetic per photon", the answer is contained in the above relation plus the way we choose to named them).
A nearly concomitant and somehow related thread is What is the science behind Red light therapy? Infared and low spectrum EM waves sounds fancy to some but is it more than heat and a red light bulb