Stability and elastic response of the most promising ground state candidate Si nanowires with less than 10 nm in diameter are comparatively studied with objective molecular dynamics coupled with non-orthogonal tight-binding and classical potential models. The computationally-expensive tight-binding treatment becomes tractable due to the substantial simplifications introduced by the presented symmetry-adapted scheme. Quantitative differences regarding stability with the classical model description are noted. Using a Wulff energy decomposition approach it is revealed that these differences are caused by the inability of the classical potential to accurately describe the interaction of Si atoms on surfaces. Differences between the results of the two atomistic treatments are also noted in the elastic response in elongation.