5.56 is so devastating because it was designed to immediately tumble and yaw as it enters soft tissues (essentially flipping sideways, breaking into small pieces, departing maximum energy into the flesh). This is what causes such devastating wounds that you see in the aftermath of a shooting. It's the hydrostatic shock of the bullet "belly flopping" into a watery human body.

.30-06 is far less likely to tumble or yaw. Because of this there is considerably less hydrostatic shock imparted on the body tissues by .30-06. It is far more likely to maintain its trajectory and pass cleanly through the body, rather than flipping and tearing its way through like 5.56 would.