  We consider the 2 Higgs Doublet Model (2HDM) and compare two effective field
theory (EFT) approaches to it, according to whether the heavy degrees of
freedom are integrated out before (SMEFT) or after (HEFT) spontaneous symmetry
breaking. %We show that, in the HEFT, an inconsistent EFT is obtained if one
considers an expansion simply in inverse powers of the heavy masses. %We
consider a HEFT expansion consistent with perturbativity %We show that, if the
HEFT approach is required to comply with perturbativity, it ends up obeying the
same power counting as the SMEFT one. % By requiring decoupling and
perturbativity in the 2HDM, we define a consistent EFT expansion in inverse
powers of the heavy masses which is applied to both the SMEFT and the HEFT
matchings to the 2HDM. We organize this expansion with a dimensionless
parameter $\xi$, and investigate the tree-level scatterings $hh\rightarrow hh$
and $WW\rightarrow hh$ up to $\mathcal{O}(\xi^2)$. We find no differences
between the HEFT and the SMEFT approaches at this order. We show scenarios
where even including dimension-8 operators of the SMEFT is insufficient to
obtain an accurate matching to the 2HDM.
