Treatment of the vortex motion in the superfluids of the inner crust and the outer core of neutron stars is a key ingredient in modelling a number of pulsar phenomena, including glitches and magnetic field evolution. After recalculating the microscopic vortex velocity in the inner crust, we evaluate the velocity for the vortices in the outer core for the first time. The vortex motion between pinning sites is found to be substantially faster in the inner crust than in the outer core, v(0)(crust) similar to 10(7) cm s(-1) >> v(0)(core) similar to 1 cm s(-1). One immediate result is that vortex creep is always in the nonlinear regime in the outer core in contrast to the inner crust, where both nonlinear and linear regimes of vortex creep are possible. Other implications for pulsar glitches and magnetic field evolution are also presented.