Polymeric fibers and nonwoven polymeric fabrics having improved softness characteristics are provided. The fibers and fabrics include either a random propylene copolymer or a blend of a polypropylene polymer and a low-density polyethylene polymer. The random propylene copolymer is produced through metallocene-catalyzed and Z-N polymerization and includes from 80 wt. % to 98 wt. % of propylene-derived units and from 2 wt. % to 20 wt. % ethylene-derived units. The low-density polyethylene polymer is also produced through metallocene-catalyzed polymerization and has a melt index of greater than 10 and a molecular weight distribution of 1.5 to 4. The fibers may be produced using a variety of processes including melt blowing, melt spinning, and spunbonding. The fibers may be converted into nonwoven fabrics through conventional techniques.