A comprehensive, three-dimensional drift model is used to study the solar modulation of cosmic-ray protons and particularly of anti-protons. Spectra for protons and anti-protons from 10 MeV to 70 GeV are computed based on revisited local interstellar spectra for these particles. This is done for a complete solar cycle from 2006 to 2017, which includes the prolonged deep solar minimum period of 2006--2009 and the magnetic polarity reversal period of Oct 2012 to April 2014. The study highlights the modulation differences between these particles and addresses the level of particle drifts that is required to explain in detail the observed ant-proton to proton ratio, especially for the reversal period.