In controlling uncertain processes, it is decisive to utilize information provided by measurements in order to estimate parameters and states. Nonlinear Model Predictive Control (NMPC) is a popular method to implement feedback control and deal with uncertainties. Conventional NMPC or nominal control, however, sometimes does not provide enough information for system estimation, leading to unsatisfactory performance. Dual control attempts to strike a balance between the two goals of enhancing system estimation and optimizing the nominal objective function. In this paper, we analyze the performance of these strategies through the interplay between the performance control task and the information gain task in connection with Optimal Experimental Design. Examples illustrate the conflict and agreement between the two tasks and explain why in some cases nominal control performs well. It is also observed that measurement noise provides excitation helping to improve the quality of estimates.