  We analyze the ratio of branching ratios R=BR(H->b b-bar)/BR(H->tau^+ tau^-)
of Higgs boson decays as a discriminant quantity between supersymmetric and
non-supersymmetric models. This ratio receives large renormalization-scheme
independent radiative corrections in supersymmetric models at large \tan\beta,
which are absent in the Standard Model or Two-Higgs-doublet models. These
corrections are insensitive to the supersymmetric mass scale. A detailed
analysis in the effective Lagrangian approach shows that, with a measurement of
+-21% accuracy, the Large Hadron Collider can discriminate between models if
the CP-odd Higgs boson mass is below 900 GeV. An e+e- Linear Collider at 500
GeV center of mass energy can discriminate supersymmetric models up to a CP-odd
Higgs mass of ~ 1.8 TeV.
