We have shown that both the morphology and elongation mechanism of GaN nanowires homoepitaxially grown by plasma-assisted molecular beam epitaxy (PA-MBE) on a [0001]-oriented GaN nanowire template are strongly affected by the nominal gallium/nitrogen flux ratio as well as by additional Ga flux diffusing from the side walls. Nitrogen-rich growth conditions are found to be associated with a surface energy-driven morphology and reduced Ga diffusion on the (0001) plane. This leads to random nucleation on the (0001) top surface and preferential material accumulation at the periphery. By contrast, gallium-rich growth conditions are characterized by enhanced Ga surface diffusion promoting a kinetically driven morphology. This regime is governed by a potential barrier that limits diffusion from the top surface toward nanowire side walls, leading to a concave nanowire top surface morphology. Switching from one regime to the other can be achieved using the surfactant effect of an additional In flux. The optical properties are found to be strongly affected by growth mode, with point defect incorporation and stacking fault formation depending on gallium/nitrogen flux ratio.