In this paper, we present calculations of the hole transport properties of bulk zinc-blende and wurtzite phase GaN at field strengths at which impact ionization does not occur significantly. The calculations are made using an ensemble Monte Carlo simulator, including the full details of the band structure and a numerically determined phonon scattering rate based on an empirical pseudopotential method. Band intersection points - including band crossings and band mixings - are treated by carefully evaluating the overlap integral between the initial and possible final drift states. In this way, the hole trajectories in phase space can be accurately traced. It is found that the average hole energies are significantly lower than the corresponding electron energies for the field strengths examined. This result is most probably due to the drastic difference in curvature between the uppermost valence bands and the lowest conduction band. The relatively flat valence bands impede hole-heating, leading to low average hole energy.