In this work, we compare the performance of two structural indicators based on the degree of translational order up to the second coordination shell in three water models: SPC/E, TIP4P/2005, and TIP5P. Beyond directly contrasting their distributions for different temperatures to evidence their usefulness in estimating the fraction of structured and unstructured molecules and, when possible, their classification capability, we also correlate them with an indirect measure of structural constraint: the dynamic propensity. Furthermore, this procedure enables us to show the existence of evident correlations between structural and dynamical information. More specifically, we find that locally structured molecules display a preference for low dynamic propensity values and, more conspicuously, that locally unstructured molecules are extremely subject to high dynamic propensity. This result is particularly relevant for the supercooled regime where the establishment of firm links between the structure and dynamics has remained rather elusive since the occurrence of dynamics that vary in orders of magnitude upon supercooling usually contrast with barely noticeable overall structural changes.