If we consider the 126 Higgs-like boson as a pseudo-Nambu-Goldstone boson, what are the experimental fingerprints of that case? What are the main differences, in a purely effective field theory approach and/or "new physics" scenario with respect to the fundamental and boring Standard Model Higgs (take it as a neutral singlet, without loss of generality)?
Have a look at this publication.
Resonance at 125 GeV: Higgs or Dilaton/Radion? Zackaria Chacko, Roberto Franceschini, Rashmish K. Mishra (Submitted on 14 Sep 2012 (v1), last revised 2 Apr 2013 (this version, v2))
We consider the possibility that the new particle that has been observed at 125 GeV is not the Standard Model (SM) Higgs, but instead the dilaton associated with an approximate conformal symmetry that has been spontaneously broken. We focus on dilatons that arise from theories of technicolor, or from theories of the Higgs as a pseudo-Nambu-Goldstone boson (pNGB), that involve strong conformal dynamics in the ultraviolet. In the pNGB case, we are considering a framework where the Higgs particle is significantly heavier than the dilaton and has therefore not yet been observed. In each of the technicolor and pNGB scenarios, we study both the case when the SM fermions and gauge bosons are elementary, and the case when they are composites of the strongly interacting sector. Our analysis incorporates conformal symmetry violating effects, which are necessarily present since the dilaton is not massless, and is directly applicable to a broad class of models that stabilize the weak scale and involve strong conformal dynamics. Since the AdS/CFT correspondence relates the radion in Randall-Sundrum (RS) models to the dilaton, our results also apply to RS models with the SM fields localized on the infrared brane, or in the bulk. We identify the parameters that can be used to distinguish the dilatons associated with the several different classes of theories being considered from each other, and from the SM Higgs. We perform a fit to all the available data from several experiments and highlight the key observations to extract these parameters. We find that at present, both the technicolor and pNGB dilaton scenarios provide a good fit to the data, comparable to the SM Higgs. We indicate the future observations that will help to corroborate or falsify each scenario.
Bold mine, to high light that at the moment one cannot exclude other hypothesis to the SM Higgs. More data and accurate branching ratios should do it.