Recent experiments on face-centered cubic (fcc) and hexagonal close packed (hcp) nanocrystalline metals reported an increase of more than 10-fold in strain-rate sensitivity in contrast to their conventional coarse-grained counterparts. To improve our understanding of this issue, we consider a mesoscopic continuum model of a two-dimensional polycrystal with deformation mechanisms including grain interior plasticity, grain-boundary diffusion and grain-boundary sliding. The model captures the transition from sliding- and diffusion-dominated creep in nanocrystals with relatively small grain sizes at low strain rates to plasticity-dominated flow in nanocrystals with larger grain sizes at higher strain rates. The strain-rate sensitivity obtained from our calculations matches well with the experimental data for nanocrystalline Cu. Based on this analysis, an analytical model incorporating the competition between grain interior plasticity and grain-boundary deformation mechanisms is proposed to provide an intuitive understanding of the transition in strain-rate sensitivity in nanostructured metals.