  As the most important discovery channel for a light Higgs boson at the LHC,
the di-photon signal $gg->h->\gamma\gamma$ is sensitive to underlying physics.
In this work we investigate such a signal in a comparative way by considering
three different supersymmetric models, namely the minimal supersymmetric
standard model (MSSM), the next-to-minimal supersymmetric standard model
(NMSSM) and the nearly minimal supersymmetric standard model (nMSSM). Under the
current collider and cosmological constraints we scan over the parameter space
and obtain the following observation in the allowed parameter space: (i) In the
nMSSM the signal rate is always suppressed; (ii) In the MSSM the signal rate is
suppressed in most cases, but in a tiny corner of the parameter space it can be
enhanced (maximally by a factor of 2); (iii) In the NMSSM the signal rate can
be enhanced or suppressed depending on the parameter space, and the enhancement
factor can be as large as 7.
