  We perform a comparison, object-by-object and statistically, between the
Munich semi-analytical model, L-Galaxies, and the IllustrisTNG hydrodynamical
simulations. By running L-Galaxies on the IllustrisTNG dark matter-only merger
trees, we identify the same galaxies in the two models. This allows us to
compare the stellar mass, star formation rate and gas content of galaxies, as
well as the baryonic content of subhaloes and haloes in the two models. We find
that both the stellar mass functions and the stellar masses of individual
galaxies agree to better than $\sim0.2\,$dex. On the other hand, specific star
formation rates and gas contents can differ more substantially. At $z=0$ the
transition between low-mass star-forming galaxies and high-mass, quenched
galaxies occurs at a stellar mass scale $\sim0.5\,$dex lower in IllustrisTNG
than in L-Galaxies. IllustrisTNG also produces substantially more quenched
galaxies at higher redshifts. Both models predict a halo baryon fraction close
to the cosmic value for clusters, but IllustrisTNG predicts lower baryon
fractions in group environments. These differences are due primarily to
differences in modelling feedback from stars and supermassive black holes. The
gas content and star formation rates of galaxies in and around clusters and
groups differ substantially, with IllustrisTNG satellites less star-forming and
less gas-rich. We show that environmental processes such as ram-pressure
stripping are stronger and operate to larger distances and for a broader host
mass range in IllustrisTNG. We suggest that the treatment of galaxy evolution
in the semi-analytic model needs to be improved by prescriptions which capture
local environmental effects more accurately.
