The study of the Berezinskii-Kosterlitz-Thouless (BKT) transition in two-dimensional φ4 models can be performed in several representations, and the amplitude-phase (AP) Madelung parametrization is the natural way to study the contribution of density fluctuations to non-universal quantities. We show how one can obtain a consistent phase diagram in the AP representation using the functional renormalization group scheme. Constructing the mapping between φ4 and the XY models allows us to treat these models on equal footing. We estimate universal and non-universal quantities of the two models and find good agreement with available Monte Carlo results. The presented approach is flexible enough to treat parameter ranges of experimental relevance.