There is growing evidence that supermassive black holes may play a crucial role for galaxy evolution, in particular during the formation of massive galaxies at high redshift (z ~ 2 - 3). Our work focuses on quantifying the effects of jets of radiogalaxies and of large bolometric luminosities of quasars on the interstellar gas in their host galaxies. To this end, we studied the kinematics of the ionized gas in 12 moderately powerful radio galaxies and 11 quasars (6 radio-loud and 5 radio-quiet) at high redshifts with rest-frame optical imaging spectroscopy obtained at the VLT with SINFONI. We searched for outflows and other signatures of feedback from the supermassive black holes in the centers of these galaxies to evaluate if the AGN may plausibly quench star formation. In our sample of moderately powerful radiogalaxies, we observe velocity dispersions nearly as large as those observed in the most powerful ones (with FWHM ~ 1000 km/s), but the quantity of ionized gas is decreased by one order of magnitude (Mion gas ~ 10^8 - 10^9 Msun) and velocity gradients tend to be less dramatic (Δv < 400 km/s), when they are observed. In our sample of quasars, we had to carefully subtract the broad spectral component of emission lines to have access to its narrow, and spatially extended, component. We detect truly extended emission line regions in 4/6 sources of our radio-loud subsample and in 1/5 source of our radio-quiet subsample. We estimate that masses of ionized gas in these sources are smaller than in our sample of high-redshift radiogalaxies (with Mion gas ~ 10^7 - 10^8 Msun) and kinematics tend to be more quiescent, akin to what is observed in local quasars. Finally, detailed observations of two outliers among our sample of high-redshift radiogalaxies revealed that one of them is closely surrounded by 14 companions galaxies, hence lying in an overdensity. We therefore interpret the presence and morphology of ionized gas around these galaxies as evidence for repeated cycles ouf AGN outbursts, akin to what can be observed in local clusters of galaxies, which are prime examples of AGN feedback in the nearby Universe.