Plasmonic nanocavities with sub-5-nm gaps between nanoparticles support multiple resonances possessing ultra-high-field confinement and enhancements. Here we systematically compare the two fundamentally different resonant gap modes: transverse waveguide (s) and antenna modes (l), which, despite both tightly confining light within the gap, have completely different near-field and far-field radiation patterns. By varying the gap size, both experimentally and theoretically, we show how changing the nanoparticle shape from sphere to cube alters coupling of s and l modes, resulting in strongly hybridized (j) modes. Through rigorous group representation analysis we identify their composition and coupling. This systematic analysis of the Purcell factors shows that modes with optical field perpendicular to the gap are best to probe the optical properties of cavity-bound emitters, such as single molecules.