School choice aims to improve (1) the matching between children and schools and (2) students' educational outcomes. Yet, the concern is that disadvantaged families are less able to exercise choice, which raises (3) equity concerns. The Boston mechanism (BM) is a procedure that is widely used around the world to resolve overdemands for particular schools by defining a set of priority points based on neighborhood and socioeconomic characteristics. The mechanism design literature has shown that under the BM, parents may not have incentives to provide their true preferences, thereby establishing a trade-off between preferences and perceived safety. However, the set of possible Nash equilibria arising from the BM is large and has varying properties, and what will actually happen is an empirical question. We exploit an unexpected change in the definition of neighborhood in Barcelona, which provides an exogenous change in the set of schools perceived as safe and allows us to separate housing and schooling decisions to assess the importance of this trade-off in the data. We find that safety carries a large weight in family choice. The huge majority of parents opt for schools for which they have the highest priority the neighborhood schools excluding other preferred schools. Similar to the previous literature, we also find that some parents seem naive, but using school registry data, we find that a significant fraction of them have the outside option of private schools, which allows them to take higher risks to access the best public schools. At the other extreme, some of the naive are not matched to any of the schools they applied for. Our results suggest that when allowing school choice under the BM with priorities: (1) the gains in terms of matching seem limited, because the equilibrium allocation is not very different from a neighborhood-based assignment, (2) estimating the effect of choice on outcomes by implementing such a mechanism may lead to a lower bound on the potential effects of having choice, and (3) important inequalities emerge beyond parents' naivete found in the literature.