The effect of the ratio between the outer and inner velocities on the vorticity dynamics and mixing in the initial stage of development of coaxial jet flows is analyzed through axisymmetric numerical simulations. For relatively low values of the velocity ratio (in all cases greater than unity), the vorticity dynamics is dominated by the large positive startup vortex forming from the external shear-layer. As the velocity ratio increases, the roll-up of the internal negative vorticity layer produces a vortical structure comparable in intensity and size with the positive outer vortex. Thus, the mutual induction becomes more important in the dynamics of the startup vortices. The local mixing process also noticeably changes with the velocity ratio. Favorable features are observed for high velocity ratio, and, in particular, high mixing occurs between the streams near the jet outlet. Three-dimensional simulations carried out for a low value of the velocity ratio, indicate that azimuthal instabilities do not have a significant effect on the vorticity dynamics in the initial stages of the flow development.