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We report a systematic comparison of niobium nitride thin films deposited on oxidized silicon substrates by reactive DC magnetron sputtering and reactive high-power impulse magnetron sputtering (HiPIMS). After determining the nitrogen gas concentration that produces the highest superconducting critical temperature for each process, we characterize the dependence of the critical temperature on film thickness. The optimal nitrogen concentration is higher for HiPIMS than for DC sputtering, and HiPIMS produces higher critical temperatures for all thicknesses studied. We attribute this to the HiPIMS process enabling the films to get closer to optimal stoichiometry before beginning to form a hexagonal crystal phase that reduces the critical temperature, along with the extra kinetic energy in the HiPIMS process improving crystallinity. We also study the ability to increase the critical temperature of the HiPIMS films through the use of an aluminum nitride buffer layer and substrate heating.