  We analyse spatially-resolved deep optical spectroscopy of Brightest Cluster
Galaxies (BCGs) located in 32 massive clusters with redshifts of 0.05 $\leq z
\leq$ 0.30, to investigate their velocity dispersion profiles. We compare these
measurements to those of other massive early-type galaxies, as well as central
group galaxies, where relevant. This unique, large sample extends to the most
extreme of massive galaxies, spanning M$_{K}$ between -25.7 to -27.8 mag, and
host cluster halo mass M$_{500}$ up to 1.7 $\times$ 10$^{15}$ M$_{\odot}$. To
compare the kinematic properties between brightest group and cluster members,
we analyse similar spatially-resolved long-slit spectroscopy for 23 nearby
Brightest Group Galaxies (BGGs) from the Complete Local-Volume Groups Sample
(CLoGS). We find a surprisingly large variety in velocity dispersion slopes for
BCGs, with a significantly larger fraction of positive slopes, unique compared
to other (non-central) early-type galaxies as well as the majority of the
brightest members of the groups. We find that the velocity dispersion slopes of
the BCGs and BGGs correlate with the luminosity of the galaxies, and we
quantify this correlation. It is not clear whether the full diversity in
velocity dispersion slopes that we see is reproduced in simulations.
