Modern hydrodynamical simulations reproduce many properties of the real Universe. These simulations model various physical processes, but many of these are included using 'subgrid models' due to resolution limits. Although different subgrid models have been successful in modelling the effects of supernovae (SNe) and active galactic nuclei (AGNs) feedback on galactic properties, it remains unclear if, and by how much, these differing implementations affect observable halo gas properties. In this work, we use 'zoom-in' cosmological initial conditions of two volumes selected to resemble the Local Group (LG) evolved with both the AURIGA and APOSTLE galaxy formation models. While the subgrid physics models in both simulations reproduce realistic stellar components of L⋆ galaxies, they exhibit different gas properties. Namely, AURIGA predicts that the Milky Way is almost baryonically closed, whereas APOSTLE suggests that only half of the expected baryons reside within the halo. Furthermore, APOSTLE predicts that this baryon deficiency extends to the LG (r ≤ 1 Mpc). Some of the baryon deficiency in APOSTLE is due to SNe feedback at high redshift, which generates halo-wide outflows, with high covering fractions and radial velocities, which both eject baryons and significantly impede cosmic gas accretion. Conversely, in AURIGA, gas accretion into the halo appears to be almost unaffected by feedback. These differences appear to result from the different energy injection methods from feedback (both SNe and AGNs) to gas. Our results suggest that both quasar absorption lines and fast radio burst dispersion measures could constrain these two regimes with future observations.