  Beyond the Standard Model (SM) extensions usually include extended Higgs
sectors. Models with singlet or doublet fields are the simplest ones that are
compatible with the $\rho$ parameter constraint. The discovery of new non-SM
Higgs bosons and the identification of the underlying model requires dedicated
Higgs properties analyses. In this paper, we compare several Higgs sectors
featuring 3 CP-even neutral Higgs bosons that are also motivated by their
simplicity and their capability to solve some of the flaws of the SM. They are:
the SM extended by a complex singlet field (CxSM), the singlet extension of the
2-Higgs-Doublet Model (N2HDM), and the Next-to-Minimal Supersymmetric SM
extension (NMSSM). In addition, we analyse the CP-violating 2-Higgs-Doublet
Model (C2HDM), which provides 3 neutral Higgs bosons with a pseudoscalar
admixture. This allows us to compare the effects of singlet and pseudoscalar
admixtures. Through dedicated scans of the allowed parameter space of the
models, we analyse the phenomenologically viable scenarios from the view point
of the SM-like Higgs boson and of the signal rates of the non-SM-like Higgs
bosons to be found. In particular, we analyse the effect of
singlet/pseudoscalar admixture, and the potential to differentiate these models
in the near future. This is supported by a study of couplings sums of the Higgs
bosons to massive gauge bosons and to fermions, where we identify features that
allow us to distinguish the models, in particular when only part of the Higgs
spectrum is discovered. Our results can be taken as guidelines for future LHC
data analyses, by the ATLAS and CMS experiments, to identify specific benchmark
points aimed at revealing the underlying model.
