Traffic control performance on networks depends on the flow response to the policy adopted, which in turn contributes to determine the optimal signal settings. This paper focuses on the relationship between local and network wide traffic control policies within the combined traffic control and assignment problem. Through a full exploration of the solution space, an in depth cross comparison is performed between the well-known local policies P0 and Equisaturation, versus the global policies Maximum Throughput and Minimum Delay, to verify how the two local policies approximate the optimal settings for signalized intersections. Realistic traffic dynamics, such as congestion, multiple controllers and spillback are considered, to empirically determine the conditions under which the local policies are able to approximate global performances. After presenting the different local and global control policies, experiments are performed on simple toy networks. The complexity of the underlying network and, therefore, of the problems' boundary conditions is then increased, allowing us to showcase how the different metrics perform in different situations. Finally, conclusions on the results are drawn.