Background: Obstructive sleep apnea (OSA) is characterized by repeated airway obstructions during sleep, causing hypopnea, apnea, intermittent hypoxia, and sleep fragmentation. The severity of OSA is measured using the apnea–hypopnea index (AHI), with AHI ≥ 5 indicating OSA. This study aims to assess the frequency and type of depressive disorder characteristics of OSA patients and to evaluate the impact on quality of life, also considering the presence of hyperactivity. Methods: A case-control study using OSA patients referred to Cagliari’s sleep disorder center. Controls were matched by age and sex from community databases. OSA diagnoses were made with AHI > 15. Depressive episodes were identified using BDI-SF, and H-QoL (Health related Quality of Life) was measured with the SF-12, focusing on item 10 for hyper-energy. Results: The clinical sample (n = 25) had a higher frequency of depressive episodes (36%) compared to controls (7% and 4%). Depressed OSA patients had worse H-QoL and higher hyper-energy scores, but the additional burden from depression was relatively low. Conclusions: The OSA sample has a higher frequency of depressive episodes compared to the general population. Depressive episodes in OSA patients are linked to higher scores on item 10 of the SF-12, indicating hyper-energy despite lower overall quality of life scores. While OSA significantly impacts quality of life, the additional burden from depression is less severe than in other chronic diseases. These findings suggest that depressive episodes in OSA may be related to rhythm dysregulation and hyperactivity (DYMERS).