Synchronization features are explored for a pair of chaotic high-dimensional bidirectionally coupled structurally nonequivalent systems. We find two regimes of synchronization in dependence on the coupling strength: creation of a lower dimensional chaotic state, and for larger coupling a transition toward a stable periodic motion. We characterize this new state, showing that it is associated with an abrupt transition in the Lyapunov spectrum. The robustness of this state against noise is discussed, and the use of this dynamical property as a possible approach for the control of chaos is outlined.