Dynamic magnetic properties (phase transition temperatures, compensation temperatures and phase diagrams) of the spin-7/2 hexagonal and cylindrical Ising nanowire systems with core-shell structure were studied by utilizing Glauber-type stochastic dynamics as well as the mean-field theory. Using different Hamiltonian parameters, thermal variations of nanowire systems' magnetizations were studied to find dynamic phase transition temperatures, dynamic compensation temperatures as well as to determine dynamic compensation behavior. The dynamic phase transitions in cylindrical Ising nanowire system were found to exist at higher temperatures than in hexagonal Ising nanowire system. Moreover, the Q-, P- and R-type compensation behaviors were observed in both Ising nanowire systems. While N-type behavior was seen only in cylindrical Ising nanowire system, S-type behavior was observed only in cylindrical Ising nanowire system. Finally, the dynamic phase diagrams of Ising nanowire systems were obtained for different planes. It is found that the dynamic phase diagram of hexagonal Ising nanowire system contains the re-entrant behavior and the dynamic triple point and the cylindrical Ising nanowire system does not include them. From all the studies, it was observed that dynamic magnetic properties of Ising nanowire systems were strongly dependent on Hamiltonian parameters.