  We examine the effect of finite top- and bottom-quark masses on the Higgs
production cross section in the gluon-gluon fusion channel. We employ both
$\overline{\text{MS}}$ and on-shell renormalisation for the quark masses and
provide a thorough comparison. Furthermore, we explore alternative treatments
of quark masses, in particular in the four-flavour scheme, and investigate
their impact on the cross section. Our work also presents novel predictions for
differential cross sections in the Higgs rapidity. The results lead to a
significant reduction of scale uncertainties, and our analysis enables us to
offer well-grounded recommendations for future research in this area.
