Despite SARS-CoV and SARS-CoV-2 being equipped with highly similar protein arsenals, the corresponding zoonoses have been spread among humans at extremely different magnitudes. The specific characteristics of these viruses that lead to distinct outcomes remains unclear. Here, we apply proteome-wide comparative structural analysis aiming to identify the unique molecular elements in the SARS-CoV-2 proteome that may be responsible for the worldwide spread of COVID-19. By combining protein modeling and molecular dynamics simulations, we suggest non-conservative substitutions in functional regions of the spike glycoprotein (S), nsp1, and nsp3 that are contributing to differences in virulence. Particularly, we explain why the substitutions at the receptor-binding domain of S affect the structure-dynamics behavior in complexes with putative host receptors. Conservation of functional protein regions within the two taxa is also noteworthy. We suggest that the highly conserved main protease, nsp5, of SARS-CoV and SARS-CoV-2 is part of their mechanism of circumventing the host interferon antiviral response. Overall, most substitutions occur on the protein surfaces and may be modulating their antigenic properties and interactions with other macromolecules. Our results imply that the striking difference in the pervasiveness of SARS-CoV-2 and SARS-CoV among humans seems to significantly derive from molecular features that modulate the efficiency of viral particles in entering the host cells and blocking the host immune response.