Background/Objectives: Respiratory syncytial virus (RSV) represents a significant cause of acute respiratory infections (ARIs) in adults aged 60 years and older, often leading to severe clinical outcomes and high healthcare costs. This study aimed to evaluate the clinical and economic burden of RSV compared to other ARIs, focusing on specific age groups, comorbidities, and demographic factors. Methods: A retrospective observational study was conducted using the electronic medical records of adults aged ≥60 years hospitalized for ARIs, including RSV, in Spain. Direct costs related to hospitalizations, intensive care unit (ICU) admissions, and treatments were analyzed. The study also assessed demographic, clinical, and comorbidity-related factors influencing the economic burden. Results: RSV infections resulted in significantly higher direct costs compared to other ARIs, particularly in patients aged 70–80 years. Comorbidities such as asthma and smoking history were associated with increased costs in RSV cases. Although ICU costs were comparable between groups, hospitalizations for RSV required longer stays and more intensive treatments, amplifying the overall economic burden. Differences in costs by age and sex highlighted the need for tailored clinical management strategies. Conclusions: RSV poses a substantial economic and clinical burden on adults aged 60 years and older, particularly in those with comorbidities. Preventive measures, such as vaccination, could reduce healthcare costs and improve outcomes in this vulnerable population. These findings support the inclusion of RSV vaccines in immunization programs, especially in aging populations like Spain, to alleviate healthcare pressures during peak respiratory disease seasons.