The presence of random arrays of elongated nanostructures with dimensional nonuniformity on the cuticular surfaces of insects endows them with antiwetting characteristics, as exemplified by nanopillar arrays on dragonfly wings and nanocone arrays on cicada wings. But the roles of the nanostructure shape and dimensional nonuniformity, as well as of the randomness of placement, on antiwetting characteristics are difficult to delineate because of the different chemical compositions of the surfaces of dragonfly and cicada wings. Therefore, biomimetic random arrays of nanopillars and nanocones with a similar tip diameter, placement irregularity, and chemical composition were fabricated on polypropylene substrates by plasma etching and polymerization. Gaussian nonuniformity of the nanopillar/nanocone dimensions as well as the irregularity of their placement were considered in determining the antiwetting capillary pressure and the adhesion energy. The gradient of the antiwetting capillary pressure normal to the substrate plane is the reason for nanocone arrays to resist wetting by water droplets impacting at high speeds much better than nanopillar arrays. The tapered shape of nanocones also promotes the dewetting transition of droplets from the sticky Wenzel state to the slippery Cassie state.