  In the study of subdiffusive wave-packet spreading in disordered Klein-Gordon
(KG) nonlinear lattices, a central open question is whether the motion
continues to be chaotic despite decreasing densities, or tends to become
quasi-periodic as nonlinear terms become negligible. In a recent study of such
KG particle chains with quartic (4th order) anharmonicity in the on-site
potential, it was shown that $q-$Gaussian probability distribution functions of
sums of position observables with $q > 1$ always approach pure Gaussians
($q=1$) in the long time limit and hence the motion of the full system is
ultimately "strongly chaotic". In the present paper, we show that these results
continue to hold even when a sextic (6th order) term is gradually added to the
potential and ultimately prevails over the 4th order anharmonicity, despite
expectations that the dynamics is more "regular", at least in the regime of
small oscillations. Analyzing this system in the subdiffusive energy domain
using $q$-statistics, we demonstrate that groups of oscillators centered around
the initially excited one (as well as the full chain) possess strongly chaotic
dynamics and are thus far from any quasi-periodic torus, for times as long as
$t=10^9$.
