Objective: The aim of this study was to investigate the relationship between age and sex in regard to the development of deep sternal wound infections and sternal instability following median sternotomy. Methods: A propensity-score-matching analysis was conducted on 4505 patients who underwent cardiac surgery between 2009 and 2021, all of whom had a BMI of ≥30 kg/m2. A total of 1297 matched pairs were determined in the sex group, and 1449 matched pairs we determined in the age group. The distributions of sex, age, diabetes mellitus, delirium, unstable sterna, wire refixation, wire removal, superficial vacuum-assisted wound closure, deep vacuum-assisted wound closure, clamp time, bypass time, logistic EuroSCORE, and BMI were determined. Results: The 30-day in-hospital mortality was found to be similar in the older and younger groups (8.149% vs. 8.35%, p = 0.947), and diabetes mellitus was also equally distributed in both groups. However, postoperative delirium occurred significantly more often in the older group (29.81% vs. 17.46%, p < 0.001), and there was a significantly higher incidence in men compared with women (16.96% vs. 26.91%, p < 0.001). There were no differences found in the incidence of sternum instability, fractured sternum, superficial vacuum-assisted wound closure, and deep vacuum-assisted wound closure between the age and sex groups. Conclusions: In conclusion, this study found that sternal instability and deep-wound-healing problems occur with equal frequency in older and younger patients and in men and women following median sternotomy. However, the likelihood of postoperative delirium is significantly higher in older patients and in men. These findings suggest that a higher level of monitoring and care may be required for these high-risk patient groups to reduce the incidence of postoperative delirium and improve outcomes following median sternotomy.