  (abridged) The third data release of Gaia, has provided stellar parameters,
metallicity [M/H], [{\alpha}/Fe], individual abundances, broadening parameter
from its RVS spectra for about 5.6 million objects thanks to the GSP-Spec
module. The catalogue publishes the radial velocity of 33 million sources. We
took advantage of the intersections between Gaia RVS and Gaia-ESO to compare
their stellar parameters, abundances and radial and rotational velocities. We
aimed at verifying the overall agreement between the two datasets, considering
the various calibrations and the quality-control flag system suggested for the
Gaia GSP-Spec parameters. For the targets in common between Gaia RVS and
Gaia-ESO, we performed several statistical checks on the distributions of their
stellar parameters, abundances and velocities of targets in common. For the
Gaia surface gravity and metallicity we considered both the uncalibrated and
calibrated values. We find an excellent agreement between the Gaia and Gaia-ESO
radial velocities given the uncertainties affecting each dataset. Less than 25
of ~2100 Gaia-ESO spectroscopic binaries are flagged as non-single stars by
Gaia. The temperature scales are in good agreement. The calibrated GSP-Spec
gravity should be preferred. We note that the quality (accuracy, precision) of
the GSP-Spec parameters degrades quickly for objects fainter than G~11. We find
that the somewhat imprecise GSP-Spec abundances due to its medium-resolution
spectroscopy over a short wavelength window and the faint G regime of the
sample under study can be counterbalanced by working with averaged quantities.
We studied some properties of the open-cluster population: our combined sample
traces very well the radial [Fe/H] and [Ca/Fe] gradients, the age-metallicity
relations in different radial regions, and it places the clusters in the thin
disc.
