On-the-fly free-energy parametrization is a new collective variable biasing approach akin to metadynamics with one important distinction: rather than acquiring an accelerated distribution via a history-dependent bias potential, sampling on this distribution is achieved from the beginning of the simulation using temperature-accelerated molecular dynamics. In the present work, we compare the performance of both approaches to compute the free-energy profile along a scalar collective variable measuring the H-bond registry of the β-sheet structure of the mouse Prion protein. Both methods agree on the location of the free-energy minimum, but free-energy profiles from well-tempered metadynamics are subject to a much higher degree of statistical noise due to hidden barriers. The sensitivity of metadynamics to hidden barriers is shown to be a consequence of the history dependence of the bias potential, and we detail the nature of these barriers for the prion β-sheet. In contrast, on-the-fly parametrization is much less sensitive to these barriers and thus displays improved convergence behavior relative to that of metadynamics. While hidden barriers are a frequent and central issue in free-energy methods, on-the-fly free-energy parametrization appears to be a robust and preferable method to confront this issue.