It is often claimed that the ~125 GeV Higgs poses a challenge for unified SUSY and forces superpartner masses well beyond 1 TeV. I will investigate whether this is true primarily in the framework of the Constrained Minimal SUSY Model (CMSSM) but also the Constrained Non-MSSM (CNMSSM) for comparison and additional options. I will apply current relevant data, including that from SUSY searches, B_s to mu+ mu- and other flavor physics as well as from dark matter relic density. I will derive resulting mass spectra for Higgs and superpartners and will discuss prospects of testing them in Run 1 of the LHC and in dark matter searches.