Examples are the Catholic Church and the armed forces. This means that the information passed up the pyramid is distorted at each level. Thus, each higher layer of managers tends to have less and less contact with reality, and near the top they are often completely out of touch. The other model might be called the network model. People are connected, but not in pyramids.
Power is distributed much more evenly.
This inspiring book gives a complete plan for building organizations that work. His goal is to make our economy efficient and competitive. The results look equally promising for application to public organizations such as schools and regulatory agencies. Another vote for redesigning the way our organizations work. I think Gandhi had some pretty good ideas.