Phonon transport in periodically modulated cylindrical nanowire (PMCN) and quasi-periodically modulated cylindrical nanowire (QPMCN) is comparatively studied. It is shown that the transmission coefficient and thermal conductance for PMCN is greater than the corresponding values for QPMCN. At low frequencies, a wide stop-frequency gap due to the destructive interference between the incoming and back waves can be clearly observed here. For PMCN, such stop-frequency gap seems to be insensitive to the change of N (the periodic number). For QPMCN, however, its breadth increases with the increase of N (the Fibonacci number). When N is increased, the thermal conductance for PMCN presents a distinct change from the decrease to the constant, while QPMCN has a tendency of monotonous decrease. A brief discussion on these results is made.