  We compare global predictions from the EAGLE hydrodynamical simulation, and
two semi-analytic (SA) models of galaxy formation, L-GALAXIES and GALFORM. All
three models include the key physical processes for the formation and evolution
of galaxies and their parameters are calibrated against a small number of
observables at $z\approx 0$. The two SA models have been applied to merger
trees constructed from the EAGLE dark matter only simulation. We find that at
$z\leq 2$, both the galaxy stellar mass functions for stellar masses
$M_*<10^{10.5} M_{\odot}$ and the median specific star formation rates (sSFRs)
in the three models agree to better than $0.4$~dex. The evolution of the sSFR
predicted by the three models closely follows the mass assembly history of dark
matter haloes. In both EAGLE and L-GALAXIES there are more central passive
galaxies with $M_*<10^{9.5} M_{\odot}$ than in L-GALAXIES. This difference is
related to galaxies that have entered and then left a larger halo and which are
treated as satellites in GALFORM. In the range $0<z<1$, the slope of the
evolution of the star formation rate density in EAGLE is a factor of $\approx
1.5$ steeper than for the two SA models. The median sizes for galaxies with
$M_*>10^{9.5} M_{\odot}$ differ in some instances by an order of magnitude,
while the stellar mass-size relation in EAGLE is a factor of $\approx 2$
tighter than for the two SA models. Our results suggest the need for a revision
of how SA models treat the effect of baryonic self-gravity on the underlying
dark matter. The treatment of gas flows in the models needs to be revised based
on detailed comparison with observations to understand in particular the
evolution of the stellar mass-metallicity relation.
