Hydraulic tomography is a state-of-the-art method for inferring hydraulic conductivity fields using head data. We employed geostatistical inversion using synthetically generated head and flux data individually and jointly in a steady-state experiment. We designed 96 inversion scenarios to better understand the relative merits of each data type. For the typical case of a small number of observation points, we find that flux data provide a better resolved hydraulic conductivity field compared to head data when considering data with similar signal-to-noise ratios. This finding is further confirmed by a resolution analysis. When considering a high number of observation points, the estimated fields are of similar quality regardless of the data type. In terms of borehole boundary conditions, the best setting for flux and head data are constant head and constant rate, respectively, while joint inversion results are insensitive to the borehole boundary type. When considering the same number of observations, the joint inversion of head and flux data does not offer advantages over individual inversions. When considering the same number of observation points and, hence, twice as many observations, the joint inversion performs better than individual inversions. The findings of this paper are useful for future planning and design of hydraulic tomography tests comprising flux and head data.