The question is hard to answer not because of its colloquial character but because it tries to establish a comparison bewteen two predictions at the TeV scale sustained by two very different theoretical frameworks :
- the prediction of supersymmetric particles is made in the context of quantum renormalizable theory with fields interacting in a Minkowski 4D space-time;
- the existence of a fine structure (two-sheets) of spacetime comes with a spectral action principle on an almost-commutative geometric setting.
Despite this fundamental difference, I think it should be interesting to compare them, debate about their mathematical and observational consistency as two effective theories at the TeV scale. I understand effective theories in a modern viewpoint.
I think it's worth emphasizing that the technical naturalness issue of the Standard Model Higgs boson exists only if one assumes that it is embedded in a larger theory that goes along the line of traditional renormalizable theories (I would appreciate to be corrected if I am wrong on this statement).
Insofar as the spectral action principle applied on a crude almost-commutative geometry and with a Planck-scale cut-off already proves to be able to deliver the Einstein-Hilbert and Yang-Mill-Higgs terms, one could expect that noncommutative geometry offers another embedding of the Standard Model to some kind of UV completion.