For example, if we "construct" two black holes with the same masses, electrical charges, and angular momenta, but will make the first black hole out of ordinary matter, and the second one out of anti-matter, they would be completely indistinguishable - none of the special particle physics pseudo-charges (baryonic, leptonic, "color, etc) is conserved in the black hole.
It should be noted, however, that not all theoreticians believe that the "no hair" holds completely. For example, Penrose argues that at least some of the information "lost" at the event horizon will be recovered during the process of black hole evaporation.