The theory of line-driven winds can explain many observed spectral features in early-type stars, though our understanding the winds of B supergiants remains incomplete. The hydrodynamic equations for slowly rotating stellar winds predict two regimes based on the line-force parameter δ: the fast and the δ-slow solution. In this paper, we aim to explore the capability of the latter to explain the observed properties of B supergiant winds. We calculate Hα line profiles, the most sensitive wind diagnostics in the optical, for both fast and δ-slow wind models. We fit them to observed data from a well-studied sample of B supergiants, by adapting the line-force parameters (k, α, and δ) of the hydrodynamic model. Unexpectedly, the observed Hα spectra can be reproduced by both hydrodynamic wind regimes with similar precision. We argue that this similarity results from the similar shape of the normalized velocity law produced by both regimes in the lower, Hα-forming wind region. Our findings raise a dichotomy, because mass-loss rates and terminal velocities (v∞) for each solution are quite different. The δ-slow solution predicts maximum values for v∞ that are systematically lower than those measured in the ultraviolet, whereas the v∞ values of the fast solution are closer, and probably more appropriate. However, our results also indicate that the δ-slow solution might better describe the dense winds of B hypergiants. Multiwavelength analyses and a larger sample of stars are needed to reach a definitive conclusion.