Fast synchronization of chaotic oscillators is important in coherent chaotic communication systems to provide the highest possible bitrate. In the current study, we consider two chaotic communication systems based on the Rössler and Lorenz chaotic oscillators, respectively, and using symmetry coefficient modulation (SCM). We estimate the synchronization times for various state variables of the systems and the different symmetry and synchronization coefficients. The experimental results show that the synchronization coefficient significantly influences the synchronization time and the particular choice of the state variable for both systems. On the contrary, the symmetry coefficient almost does not affect the synchronization time, so it can be chosen on other criteria.