  We examine the distribution of neutral hydrogen in cosmological simulations
carried out with the new moving-mesh code AREPO and compare it with the
corresponding GADGET simulations based on the smoothed particle hydrodynamics
(SPH) technique. The two codes use identical gravity solvers and baryonic
physics implementations, but very different methods for solving the Euler
equations, allowing us to assess how numerical effects associated with the
hydro-solver impact the results of simulations. Here we focus on an analysis of
the neutral gas, as detected in quasar absorption lines. We find that the high
column density regime probed by Damped Lyman-alpha (DLA) and Lyman Limit
Systems (LLS) exhibits significant differences between the codes. GADGET
produces spurious artefacts in large halos in the form of gaseous clumps,
boosting the LLS cross-section. Furthermore, it forms halos with denser central
baryonic cores than AREPO, which leads to a substantially greater DLA
cross-section from smaller halos. AREPO thus produces a significantly lower
cumulative abundance of DLAs, which is intriguingly in much closer agreement
with observations. The column density function, however, is not altered enough
to significantly reduce the discrepancy with the observed value. For the low
column density gas probed by the Lyman-alpha forest, the codes differ only at
the level of a few percent, suggesting that this regime is quite well described
by both methods, a fact that is reassuring for the many Lyman-alpha studies
carried out with SPH thus far. While the residual differences are smaller than
the errors on current Lyman-alpha forest data, we note that this will likely
change for future precision experiments.
