Addictive drug exposure is associated with impairments in various cognitive domains. Murine models of drug-induced cognitive impairment have helped to inform research on interventions to attenuate such cognitive diminishment; however, while differences between the drug-induced cognitive impairments exhibited by C57BL/6J and BALB/cJ mice have been observed, they remain unclear. This study measured differences in cognitive behavior performance on the object recognition test (ORT) and social recognition test (SRT) and serum levels of corticosterone (CORT) between C57BL/6J and BALB/cJ mice after 14-day chronic exposure to either cocaine (5 mg/kg) or morphine (3 mg/kg) at a dosage of 10 ml/kg/day. The ORT revealed that cocaine and morphine exposure significantly reduced the discrimination ratio in both C57BL/6J and BALB/cJ mice, exploration time was only reduced in C57BL/6J mice: the exploration times of C57BL/6J mice from the control (p < 0.05), cocaine (p < 0.05), and morphine (p < 0.01) administration groups were significantly less than those of BALB/cJ mice. The SRT demonstrated that drug exposure significantly reduced exploration time (cocaine, p < 0.01; morphine, p < 0.01) and impaired social recognition in C57BL/6J mice. No significant effect in BALB/cJ mice was observed. Serum CORT levels were lower in control C57BL/6J mice than in control BALB/cJ mice (p < 0.05), but no difference was observed after drug administration. In conclusion, changes in object and social learning recognition indicate that C57BL/6J mice are more sensitive than BALB/cJ mice to chronic drug exposure, especially to cocaine; concomitant changes in serum CORT may mediate these effects.