We have carried out a controlled comparison of the structural and kinematic properties of the circumgalactic medium ( CGM ) around Milky Way mass galaxies in the Illustris and IllustrisTNG simulations . Very striking differences are found . At z=0 , gas column density and temperature profiles at large radii ( \sim 100 kpc ) correlate strongly with disk gas mass fraction in Illustris , but not in TNG . The neutral gas at large radii is preferentially aligned in the plane of the disk in TNG , whereas it is much more isotropic in Illustris . The vertical coherence scale of the rotationally supported gas in the CGM is linked to the gas mass fraction of the galaxy in Illustris , but not in TNG . A tracer particle analysis allows us to show how these differences can be understood as a consequence of the different sub-grid models of feedback in the two simulations . A study of spatially matched galaxies in the two simulations shows that in TNG , feedback by supernovae and AGN helps to create an extended smooth reservoir of hot gas at high redshifts , that then cools to form a thin , rotationally-supported disk at later times . In Illustris , AGN dump heat in the form of hot gas bubbles that push diffuse material at large radii out of the halo . The disk is formed by accretion of colder , recycled material , and this results in more vertically extended gas distributions above and below the Galactic plane . We conclude that variations in the structure of gas around Milky Way mass galaxies are a sensitive probe of feedback physics in simulations and are worthy of more observational consideration in future .