The crystallization and the mechanical properties of polyethylene, which is one of the most important commodity polymers, are influenced by the crystalline alpha-relaxation. This process originates from the diffusive chain transport through the crystallites as mediated by local 180 degrees flips. Recent studies have stressed the relevance of the chain folding morphology on the chain diffusion, but its relation to the rate of jumps of the individual repeat units has not yet been addressed. In this study, we compare samples with very different morphology, including nanocrystals as a unique new model system, and use proton low-field and carbon-13 high-field solid-state NMR spectroscopy to determine the rate of local jumps and the large-scale crystalline-amorphous diffusion coefficient, respectively. We find that samples with tight folds (reactor powders and nanocrystals) display on average lower activation energies of the local jumps. Nanocrystals stand out in that they feature a significantly broader distribution of local jump rates, which we attribute to the location of stems in the finite nanocrystal. Our results for the crystalline-amorphous long-range diffusion are at partial variance with previous findings in that samples with tight folds do not generally exhibit the fastest diffusion, and we discuss the related ambiguities. Our data suggest that the higher chain mobility in the amorphous domain of melt-crystallized samples has an accelerating effect on intracrystalline chain dynamics at high temperatures but is accompanied by a more progressive slowdown at low temperatures due to cooperativity effects.