The Bayesian Dirichlet equivalent uniform (BDeu) function is a popular score to evaluate the goodness of a Bayesian network structure given complete categorical data. Despite its interesting properties, such as likelihood equivalence, it does require a prior expressed via a user-defined parameter known as Equivalent Sample Size (ESS), which significantly affects the final structure. We study conditions to obtain prior independence in BDeu-based structure learning. We show in experiments that the amount of data needed to render the learning robust to different ESS values is prohibitively large, even in big data times.