Logic styles with constant power consumption are promising solutions to counteract side-channel attacks on sensitive cryptographic devices. Recently, one vulnerability has been identified in a standard-cell-based power-constant logic called WDDL. Another logic, nicknamed SecLib, is considered and does not present the flaw of WDDL. In this paper, we evaluate the security level of WDDL and SecLib. The methodology consists in embedding in a dedicated circuit one unprotected DES coprocessor along with two others, implemented in WDDL and in SecLib. One essential part of this paper is to describe the conception of the cryptographic ASIC, devised to foster side-channel cryptanalyses, in a view to model the strongest possible attacker. The same analyses are carried out successively on the three DES modules. We conclude that, provided that the back-end of the WDDL module is carefully designed, its vulnerability cannot be exploited by the state-of-the-art attacks. Similarly, the SecLib DES module resists all assaults. However, using a principal component analysis, we show that WDDL is more vulnerable than SecLib. The statistical dispersion of WDDL, which reflects the correlation between the secrets and the power dissipation, is proved to be an order of magnitude higher than that of SecLib.