The latest years have seen steady progresses in WIMP dark matter (DM) searches, with hints of possible signals suggested by both direct and indirect detection experiments. Antiprotons can play a key role validating those interpretations since they are copiously produced by WIMP annihilations in the Galactic halo, and the secondary antiproton background produced by Cosmic Ray (CR) interactions is predicted with fair accuracy and matches the observed spectrum very well. Using the publicly available numerical DRAGON code, we reconsider antiprotons as a tool to constrain DM models discussing its power and limitations. We provide updated constraints on a wide class of annihilating DM models by comparing our predictions against the most up-to-date ap measurements, taking also into account the latest spectral information on the p, He and other CR nuclei fluxes. Doing that, we probe carefully the uncertainties associated to both secondary and DM originated antiprotons, by using a variety of distinctively different assumptions for the propagation of CRs and for the DM distribution in the Galaxy. We find that the impact of the astrophysical uncertainties on constraining the DM properties can be much stronger, up to a factor of ~50, than the one due to uncertainties on the DM distribution (~2-6). Remarkably, even reducing the uncertainties on the propagation parameters derived by local observables, non-local effects can still change DM model constraints even by 50%. Nevertheless, current ap data place tight constraints on DM models, excluding some of those suggested in connection with indirect and direct searches. Finally we discuss the power of upcoming CR spectral data from the AMS-02 observatory to drastically reduce the uncertainties discussed in this paper and estimate the expected sensitivity of this instrument to some sets of DM models.