The extant genetic machinery revolves around three interrelated polymers: RNA, DNA and proteins. Two evolutionary views approach this vital connection from opposite perspectives. The RNA World theory posits that life began in a cold prebiotic broth of monomers with the de novo emergence of replicating RNA as functionally self-contained polymer and that subsequent evolution is characterized by RNA → DNA memory takeover and ribozyme → enzyme catalyst takeover. The FeS World theory posits that life began as an autotrophic metabolism in hot volcanic-hydrothermal fluids and evolved with organic products turning into ligands for transition metal catalysts thereby eliciting feedback and feed-forward effects. In this latter context it is posited that the three polymers of the genetic machinery essentially coevolved from monomers through oligomers to polymers, operating functionally first as ligands for ligand-accelerated transition metal catalysis with later addition of base stacking and base pairing, whereby the functional dichotomy between hereditary DNA with stability on geologic time scales and transient, catalytic RNA with stability on metabolic time scales existed since the dawn of the genetic machinery. Both approaches are assessed comparatively for chemical soundness.