  We present the analysis of a suite of simulations run with different
particle-and grid-based cosmological hydrodynamical codes and compare them with
observational data of the Milky Way. This is the first study to make
comparisons of properties of galaxies simulated with particle and grid-based
codes. Our analysis indicates that there is broad agreement between these
different modelling techniques. We study the velocity dispersion - age relation
for disc stars at z=0 and find that four of the simulations are more consistent
with observations by Holmberg et al. (2008) in which the stellar disc appears
to undergo continual/secular heating. Two other simulations are in better
agreement with the Quillen & Garnett (2001) observations that suggest a
"saturation" in the heating profile for young stars in the disc. None of the
simulations have thin discs as old as that of the Milky Way. We also analyse
the kinematics of disc stars at the time of their birth for different epochs in
the galaxies' evolution and find that in some simulations old stars are born
cold within the disc and are subsequently heated, while other simulations
possess old stellar populations which are born relatively hot. The models which
are in better agreement with observations of the Milky Way's stellar disc
undergo significantly lower minor-merger/assembly activity after the last major
merger - i.e. once the disc has formed. All of the simulations are
significantly "hotter" than the Milky Way disc; on top of the effects of
mergers, we find a "floor" in the dispersion that is related to the underlying
treatment of the heating and cooling of the interstellar medium, and the low
density threshold which such codes use for star formation. This finding has
important implications for all studies of disc heating that use hydrodynamical
codes.
