  We compute the energy scales of perturbative unitarity violation in $V_L V_L
\to V_L V_L h$ processes and compare them to $V_L V_L \to hhh$ process. Using
these energy scales, we determine which process is more sensitive to potential
modifications in the Higgs sector at high-energy colliders. Within the Higgs
Effective Field Theory (HEFT), we consider the Higgs cubic coupling and other
interactions with and without derivatives. Any HEFT interactions predict the
perturbative unitarity violation at a finite scale, and in a generic case, the
minimalistic process is $2\to 3$ scattering. Our analysis reveals that the
energy scales for unitarity violation in $V_L V_L \to V_L V_L h$ and $V_L V_L
\to hhh$ processes are similar across all scenarios considered. If the
backgrounds are similar, $V_L V_L h$ final states are more feasible because
$V_L V_L h$ has higher branching ratios in cleaner decay modes than $hhh$. We
also investigate HEFT derivative interactions derived from various UV models.
In these cases, both $V_L V_L \to V_L V_L$ and $V_L V_L \to hh$ processes
exhibit unitarity violating behavior. We demonstrate that the energy scales for
unitarity violation in $V_L V_L$ final states are comparable to or even lower
than those in the $hh$ final state.
