  We calculate differential cross sections for $c \bar c$- and $b \bar b$-dijet
production in $pp$-scattering at $\sqrt{s} = 13$ TeV in the $k_T$-factorization
and hybrid approaches with different unintegrated parton distribution functions
(uPDFs). We present distributions in transverse momentum and pseudorapidity of
the leading jet, rapidity difference between the jets and the dijet invariant
mass. Our results are compared to recent LHCb data on forward production of
heavy flavour dijets, measured recently for the first time individually for
both, charm and bottom flavours. We found that an agreement between the
predictions and the data within the full $k_T$-factorization is strongly
related to the modelling of the large-$x$ behaviour of the gluon uPDFs which is
usually not well constrained. The problem may be avoided following the hybrid
factorization approach. Then a good description of the measured distributions
is obtained with the Parton-Branching, the Kimber-Martin-Ryskin, the
Kutak-Sapeta and the Jung setA0 CCFM gluon uPDFs. We calculate also
differential distributions for the ratio of $c \bar c$ and $b \bar b$ cross
sections. In all cases we obtain the ratio close to 1 which is caused by the
condition on minimal jet transverse momentum ($p_{T}^{\mathrm{jet}} > 20$ GeV)
introduced in the experiment, that makes the role of heavy quark mass almost
negligible. The LHCb experimental ratio seems a bit larger. We discuss
potentially important for the ratio effect of $c$- or $b$-quark gluon radiative
corrections related to emission outside of the jet cone. The found effect seems
rather small. More refine calculation requires full simulation of $c$- and
$b$-jets which goes beyond of the scope of the present paper.
