We combine experiments and simulations to investigate leakage current and breakdown (BD) in stoichiometric and sub-stoichiometric hafnium oxides. Using charge-transport simulations based on phonon-assisted carrier tunneling between trap sites, we demonstrate that higher currents generally observed in HfO _x are due to a higher density of the as-grown oxygen vacancy defects assisting the charge transport. Reduction of the dielectric BD field ( E _BD ) in HfO _x is explained by the lower zero-field activation energy ( E _A,G ) of the defect generation process, as extracted from time-dependent dielectric BD experiments.