The dynamical properties of two spatially coupled multi-mode lasers are investigated theoretically. When the loss of the system is modulated, the total intensities of the two lasers show perfect chaotic synchronization within certain parameter range. The intensities of the corresponding modes also show chaotic synchronization. While for different modes, the intensities are totally chaotic. The intensities of the modes in the lasers show mode competition. The phase and phase difference in each mode show very interesting relations. There is some link between the chaotic synchronization of intensities and phases.