I'm a complete noobe in physics and quite honestly need help. My question is simple, based on CERN's tentative findings stating the Higgs boson at a mass of ~125 GeV: Is the physics community leaning more towards supersymmetry or multiverse?
Yes, physics has learned things on both concepts, but only gradually.
The value of the mass 125 GeV is in the sub-130-GeV region that favors supersymmetry, or makes it necessary according to some, because the pure Standard Model predicts a catastrophically unstable vacuum for such low Higgs masses. It is also below 135 GeV which is where it should be according to the general version of the minimal supersymmetric standard model.
On the other hand, 125 GeV is higher than what the simplest models of supersymmetry – at least according to most supersymmetry phenomenologists – want to see. A value closer to 115 if not 100 GeV could be favored if one wanted to make SUSY models "really simple", at least according to the sociologically prevailing ideas about the simplicity.
The idea about the multiverse has strengthened because the Higgs is known to be both light and the only new physical phenomenon found at the LHC so far. This seems to imply that Nature doesn't care about our notion of "naturalness" – the lightness of the Higgs boson relatively to some very high energy scales such as the Planck scale is "unnatural".
The multiverse is the only concrete enough yet acceptable enough framework to "predict" unnaturally small values of parameters such as the Higgs mass, so the physicists' subjective probability (belief) that "the multiverse is needed" has increased.
None of these results are really conclusive or qualitative. There are lots of loopholes and conceivable alternatives. But among the propositions that are on the market, we may usually identify the marginal winners and losers. Ideas about low-lying, easily found supersymmetry were marginal losers; the general idea of SUSY and its impact on the Higgs mass has been a marginal winner; the concept of naturalness has lost something, and the multiverse has gained a little.
As Anna said, SUSY and the multiverse are not really mutually exclusive although the "generic" multiverse explanations indeed favor no SUSY or supersymmetry invisible at realistic colliders.
The short answer is really neither. They may actually be pulling away from both simultaneously. Read below why.
That’s because the Higgs boson coming at 125 to 126 GeV has proven supersymmetry (SUSY) wrong. SUSY was precisely predicting a Higgs boson mass of 115 GeV, or a much lower mass than the actual one. That’s the admitted position of David Kaplan and Savas Dimopoulos, two of the leading physics theorists supporting SUSY. Scientists have advanced that SUSY theory should be abandoned as the Large Hadron Collier (LHC) has not come up with any supporting evidence of its veracity despite trying hard to do so since 2010 (reference: Natalie Wolchover, November 29, 2012. “Supersymmetry Fails Test, Forcing Physics to Seek New Ideas”. Scientific American).
Meanwhile, Multiverse is not a scientific hypothesis. It speculates that there are numerous universes out there. Those are not observable. They would have each their own set of laws of physics much different than our own. As conceptualized, the Multiverse theory can’t be tested. For this reason, the majority of physics theorists state that Multiverse does not belong to the body of sciences.
One leading physics theorist, Nima Arkani-Hamed, sees it differently. And, he even came up with a Higgs boson mass threshold (140 GeV) that, in his view, would support Multiverse. However, other physicists have rebutted his logic by arguing that given the speculative nature of Multiverse there are no such relevant threshold applicable. For a threshold to be relevant you would have to experimentally prove that a Higgs Boson of 140 GeV does confirm the existence of Multiverse. That’s not going to happen.