The properties of the leader-laggard chaos synchronization (LLCS) in two mutually coupled external-cavity semiconductor lasers are studied systematically. We theoretically analyze the general conditions for the LLCS based on the symmetric operation mechanism and numerically investigate the influences of operation parameters, the mismatch robustness, the chaos pass filtering effects, the communication performance, and the security of the system. It is demonstrated that stable LLCS, which allows simultaneous bidirectional message exchange in virtue of mutual chaos pass filtering effect, can be achieved in a wide operation region; moreover, high-quality LLCS and satisfactory communication performance can be maintained under a relatively large device parameter mismatch. Compared with the isochronal chaos synchronization in the same system, LLCS provides a wider operation region, a better mismatch robustness, and a stronger chaos pass filtering effect. In addition, the investigations on the security of private key message transmission under some potential attacks indicate that the security can be enhanced by increasing the bit rate moderately, exchanging messages with different bit rates, or monitoring the LLCS.