Abstract The precision measurements of galactic cosmic-ray protons from the Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics and the Alpha Magnetic Spectrometer are reproduced using a well-established three-dimensional numerical model for the period 2006 July–2019 November. The resulting modulation parameters are applied to simulate the modulation for cosmic antiprotons over the same period, which includes the times of minimum modulation before and after 2009, the maximum modulation from 2012 to 2015, including the reversal of the Sun’s magnetic field polarity, and the approach to new minimum modulation in 2020. Apart from their local interstellar spectra, the modulation of protons and antiprotons differ in their charge sign and consequent drift pattern. The lowest proton flux was in 2014 February–March, but the lowest simulated antiproton flux is found to have been in 2015 March–April. These simulated fluxes are used to predict the proton-to-antiproton ratios as a function of rigidity. The trends in these ratios contribute to clarifying, to a large extent, the phenomenon of charge-sign dependence of heliospheric modulation during vastly different phases of the solar activity cycle. This is reiterated and emphasized by displaying so-called hysteresis loops. It is also illustrated how the values of the parallel and perpendicular mean free paths, as well as the drift scale, vary with rigidity over this extensive period. The drift scale is found to be at its lowest level during the polarity reversal period, while the lowest level of the mean free paths is found to be in 2015 March–April.