We compare the kinetic energy and momentum injection rates from intense star formation, bolometric AGN radiation, and radio jets with the kinetic energy and momentum observed in the warm ionized gas in 24 powerful radio galaxies at z ~ 2. These galaxies are among our best candidates for being massive galaxies near the end of their active formation period, when intense star formation, quasar activity, and powerful radio jets all co-exist. All galaxies have VLT/SINFONI imaging spectroscopy of the rest-frame optical line emission, showing extended emission-line regions with large velocity offsets (up to 1500 km s-1) and line widths (typically 800–1000 km s-1) consistent with very turbulent, often outflowing gas. As part of the HeRGÉ sample, they also have FIR estimates of the star formation and quasar activity obtained with Herschel/PACS and SPIRE, which enables us to measure the relative energy and momentum release from each of the three main sources of feedback in massive, star-forming AGN host galaxies during their most rapid formation phase. We find that star formation falls short by factors 10−1000 of providing the energy and momentum necessary to power the observed gas kinematics. The obscured quasars in the nuclei of these galaxies provide enough energy and momentum in about half of the sample, however, only if both are transferred to the gas relatively efficiently. We compare with theoretical and observational constraints on the efficiency of the energy and momentum transfer from jet and AGN radiation, which favors the radio jets as main drivers of the gas kinematics.