We investigate the role of non shear stress and shear stressed based detachment rate functions for the longterm behavior of one-dimensional biofilm models. We find that the particular choice of a detachment rate function can affect the model prediction of persistence or washout of the biofilm. Moreover, by comparing biofilms in three settings: (i) Couette flow reactors, (ii) Poiseuille flow with fixed flow rate and (iii) Poiseuille flow with fixed pressure drop, we find that not only the bulk flow Reynolds number but also the particular mechanism driving the flow can play a crucial role for longterm behavior. We treat primarily the single species-case that can be analyzed with elementary ODE techniques. But we show also how the results, to some extent, can be carried over to multi-species biofilm models, and to biofilm models that are embedded in reactor mass balances.