The recent discovery of a Higgs-like boson at the LHC with a mass of 126 GeV has revived the interest in supersymmetric models, which predicted a Higgs boson mass below 130 GeV long before its discovery. We compare systematically the allowed parameter space in the constrained Minimal Supersymmetric Standard Model (CMSSM) and the Next-to-Minimal Supersymmetric Model (NMSSM) by minimizing the chi^2 function with respect to all known constraints from accelerators and cosmology using GUT scale parameters. For the CMSSM the Higgs boson mass at tree level is below the Z^0 boson mass and large radiative corrections are needed to obtain a Higgs boson mass of 126 GeV, which requires stop squark masses in the multi-TeV range. In contrast, for the NMSSM light stop quarks are allowed, since in the NMSSM at tree level the Higgs boson mass can be above the Z^0 boson mass from mixing with the additional singlet Higgs boson. Predictions for the scalar boson masses are given in both models with emphasis on the unique signatures of the NMSSM, where the heaviest scalar Higgs boson decays in the two lighter scalar Higgs bosons with a significant branching ratio, in which case one should observe double Higgs boson production at the LHC. Such a signal is strongly suppressed in the CMSSM. In addition, since the LSP is higgsino-like, Higgs boson decays into LSPs can be appreciable, thus leading to invisible Higgs decays.
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