It is still an open question whether the new scalar particle discovered at the LHC with a mass of 125 GeV is the SM Higgs boson or belongs to models of new physics with an extended Higgs sector, as the MSSM or 2HDM. The ratio of branching fractions R = BR(H→bb¯)/BR(H→τ+τ−) of Higgs-boson decays is a powerful tool in distinguishing the MSSM Higgs sector from the SM or non-supersymmetric 2HDM. This ratio receives large renormalization-scheme independent radiative corrections in supersymmetric models at large tanβ, which are insensitive to the SUSY mass scale and absent in the SM or 2HDM. Making use of the current LHC data and the upcoming new results on Higgs couplings to be reported by ATLAS and CMS collaborations and in a future linear collider, we develop a detailed and updated study of this ratio R which improves previous analyses and sets the level of accuracy needed to discriminate between models.