  We perform a comparative study of different types of dynamical dark energy
models (DDES) using the cosmographic method. Among the models being examined
herein we have the Running Vacuum models (RVMs), which have demonstrated
considerable ability to fit the overall cosmological data at a level comparable
to the standard cosmological model, $\Lambda$CDM, and capable of alleviating
the $\sigma_8$ and $H_0$ tensions. At the same time we address a variety of
Holographic dark energy models (HDEs) with different options for the time
(redshift)-varying model parameter $c=c(z)$. We deal with the HDEs under the
double assumption of fixed and evolving holographic length scale and assess
which one is better. Both types of DDEs (RVMs and HDEs) are confronted with the
most robust cosmographic data available, namely the Pantheon sample of
supernovae (SnIa), the baryonic acoustic oscillation data (BAOs) extracted from
measurement of the power spectrum and bispectrum of the BOSS data release, and
the cosmic chronometer measurements of the Hubble rate (CCHs) at different
redshifts obtained from spectroscopic observations of passively evolving
galaxies. Using these data samples we assess the viability of the mentioned
DDEs and compare them with the concordance $\Lambda$CDM model. From
cosmographic analysis we conclude that the RVMs fare comparably well to the
$\Lambda$CDM, a fact which adds up more credit to their sound phenomenological
status. In contrast, while some of the HDEs are favored using the current
Hubble horizon as fixed holographic length, they become highly unfavoured in
the more realistic case when the holographic length is dynamical and evolves as
the Hubble horizon.
