A comprehensive three-dimensional (3D) numerical drift model is used to compute the modulation of cosmic ray protons and anti-protons in the heliosphere. This is done using the latest development in deriving diffusion coefficients and cosmic ray interstellar spectra. Emphasis is placed on the effects of the spatial dependence of the scattering parameter, ωτ, with ω the gyro-frequency and τ a time scale defined by diffusive scattering, on the drift coefficient in the modulation of the mentioned species. A comparison of the numerical modelling of the ratio of anti-protons to protons obtained from different scenarios of ωτ is made over a solar cycle. It is found that effects of the spatial dependence of ωτ on the drift scale in the subsequent anti-proton to proton ratio are more prominent in the A > 0 solar magnetic polarity cycle. This charge-sign dependent modulation study should assist in establishing the amount of drifts observed at Earth from minimum to maximum solar activity during both polarity cycles.