  We examine the chemical properties of 5 cosmological hydrodynamical
simulations of an M33-like disc galaxy which have been shown to be consistent
with the morphological characteristics and bulk scaling relations expected of
late-type spirals. These simulations are part of the Making Galaxies In a
Cosmological Context (MaGICC) Project, in which stellar feedback is tuned to
match the stellar mass -- halo mass relationship. Each realisation employed
identical initial conditions and assembly histories, but differed from one
another in their underlying baryonic physics prescriptions, including (a) the
efficiency with which each supernova energy couples to the ISM, (b) the impact
of feedback associated with massive star radiation pressure, (c) the role of
the minimum shut-off time for radiative cooling of Type II SNe remnants, (d)
the treatment of metal diffusion, and (e) varying the IMF. Our analysis
focusses on the resulting stellar metallicity distribution functions (MDFs) in
each simulated (analogous) `solar neighbourhood' and central `bulge' region. We
compare the simulated MDFs' skewness, kurtosis, and dispersion (inter-quartile,
inter-decile, inter-centile, and inter-tenth-percentile regions) with that of
the empirical solar neighbourhood MDF and Local Group dwarfs. We find that the
MDFs of the simulated discs are more negatively skewed, with higher kurtosis,
than those observed locally. We can trace this difference to the simulations'
tight and correlated age-metallicity relations (compared with that of the Milky
Way), suggesting that these relations within `dwarf' discs might be steeper
than in L* discs and/or the degree of stellar orbital re-distribution and
migration inferred locally has not been captured in their entirety, at the
resolution of our simulations. The important role of metal diffusion in
ameliorating the over-production of extremely metal-poor stars is highlighted.
