  In this work the vector boson scattering process is investigated through the
reaction $pp\rightarrow 2 \mathrm{jets} + W^\ast W^\ast \rightarrow 2
\mathrm{jets} + l\nu_l l'\nu_l'$, where $W^\ast$ denote in general off-shell
$W^+$, in the EFT approach with the HL-LHC and HE-LHC experiments in mind. We
have investigated the discovery potential of certain classes of the EFT
"models" of both the SMEFT and HEFT bases with the particular emphasis on using
the EFT "models" in their region of validity. A novel method has been proposed
for determining the discovery regions of physics beyond the SM, described by
the EFT "models". Independent of the basis chosen, the discovery regions are
found to be non-empty. We then compare differences in experimental signatures
between SMEFT and HEFT, which is an important step for distinguishing between
the two hypotheses in the future data. Finally, we investigated what the effect
on the discovery regions is when increasing the $pp$ collision energy.
