Modern theories of galaxy formation predict that galaxies impact on their gaseous surroundings, playing the fundamental role of regulating the amount of gas converted into stars. While star-forming galaxies are believed to provide feedback through galactic winds, Quasi-Stellar Objects (QSOs) are believed instead to provide feedback through the heat generated by accretion onto a central supermassive black hole. A quantitative difference in the impact of feedback on the gaseous environments of star-forming galaxies and QSOs has not been established through direct observations. Using the Sherwood cosmological simulations, we demonstrate that measurements of neutral hydrogen in the vicinity of star-forming galaxies and QSOs during the era of peak galaxy formation show excess Lyman-α absorption extending up to comoving radii of ∼150 kpc for star-forming galaxies and 300 − 700 kpc for QSOs. Simulations including supernovae-driven winds account for the absorption around star-forming galaxies but not QSOs.