This depends on what, exactly, you mean by “economic principles.” Some economic principles apply equally in both types of organizations. Others apply to some degree in both, but apply more strongly to private organizations.
One set of economic principles has to do with how people make choices. Economists believe, for example, that people act rationally and that they respond to economic incentives. These principles apply equally to public and private organizations. This is why, for example, many American conservatives want to tie teacher pay to student performance. They believe that teachers will respond to this economic incentive by doing a better job of educating their students. These are principles that are based in human nature and govern individual human behaviors. Because human nature is the same in public and private organizations, these principles apply to both equally.
A second set of economic principles has to do with the behaviors of the organizations as a whole. These principles do not apply as strongly to the public sector. This is because the public sector is not as subject to market forces as the private sector is. For example, economic principles state that organizations will not keep workers on staff if the workers are not creating value that is equal to the cost of employing them. Economic principles also state that organizations will not continue to follow policies or procedures that do not help them achieve their goals. These principles are less true in the public sector than in the private sector. In the private sector, firms that violate these principles will be uncompetitive and will eventually have to close. Therefore, firms that wish to succeed will follow the principles. By contrast, public organizations do not generally get closed because they lose money. An example of this is the Amtrak system. It can afford to keep losing money because it is supported by the government. Because public organizations cannot be punished by market forces, economic principles do not always apply to their decisions.
In short, we can say that individual behavior is governed by economic principles in both public and private organizations. However, we can also say that organizational behavior in public organizations is less governed by economic principles than organizational behavior in private organizations.