  We study the two main constituent galaxies of a constrained simulation of the
Local Group as candidates for the Milky Way (MW) and Andromeda (M31). We focus
on the formation of the stellar discs and its relation to the formation of the
group as a rich system with two massive galaxies, and investigate the effects
of mergers and accretion as drivers of morphological transformations. We use a
state-of-the-art hydrodynamical code which includes star formation, feedback
and chemical enrichment to carry out our study. We run two simulations, where
we include or neglect the effects of radiation pressure from stars, to
investigate the impact of this process on the morphologies and star formation
rates of the simulated galaxies. We find that the simulated M31 and MW have
different formation histories, even though both inhabit, at z=0, the same
environment. These differences directly translate into and explain variations
in their star formation rates, in-situ fractions and final morphologies. The
M31 candidate has an active merger history, as a result of which its stellar
disc is unable to survive unaffected until the present time. In contrast, the
MW candidate has a smoother history with no major mergers at late times, and
forms a disc that grows steadily; at z=0 the simulated MW has an extended,
rotationally-supported disc which is dominant over the bulge. Our two feedback
implementations predict similar evolution of the galaxies and their discs,
although some variations are detected, the most important of which is the
formation time of the discs: in the model with weaker/stronger feedback the
discs form earlier/later. In summary, by comparing the formation histories of
the two galaxies, we conclude that the particular merger/accretion history of a
galaxy rather than its environment at the LG-scales is the main driver of the
formation and subsequent growth or destruction of galaxy discs.
