We have made detailed comparison of the local and chain dynamics of a melt of 1,4-polybutadiene (PBD) as determined from experiment and molecular dynamics simulation at 353 K. The PBD was found to have a random microstructure consisting of 40% cis, 50% trans, and 10% 1,2-vinyl units with a number-average degree of polymerization (X-n) = 25.4. Local (conformational) dynamics were studied via measurements of the C-13 NMR spin-lattice relaxation time T-1 and the nuclear Overhauser enhancement (NOE) at a proton resonance of 300 MHz for 12 distinguishable nuclei. Chain dynamics were studied on time scales up to 22 ns via neutron spin-echo (NSE) spectroscopy with momentum transfers ranging from q = 0.05 to 0.30 Angstrom(-1). Molecular dynamics simulations of a 100 carbon (X-n = 25) PBD random copolymer of 50% trans and 50% cis units employing a quantum chemistry-based united atom potential function were performed at 353 K. The T-1 and NOE values obtained from simulation, as well as the center of mass diffusion coefficient and dynamic structure factor, were found to be in qualitative agreement with experiment. However, comparison of T1 and NOE values for the various distinguishable resonances revealed that the local dynamics of the simulated chains were systematically too fast, whereas comparison with the center of mass diffusion coefficient revealed a similar trend in the chain dynamics. To improve agreement with experiment, (1) the chain length was increased to match the experimental M-z, (2) vinyl units groups were included in the chain microstructure, and (3) rotational energy barriers were increased by 0.4 kcal/mol in order to reduce the rate of conformational transitions. With these changes, dynamic properties from simulation were found to differ 20-30% or less from experiment, comparable to the agreement seen in previous simulations of polyethylene using a quantum chemistry-based united atom potential.