Background/Objectives: Hospital performance is a multidimensional construct that cannot be adequately assessed using isolated financial, clinical, organizational, or patient-reported indicators. This study aimed to develop and evaluate an Integrated Multidimensional Hospital Performance Assessment Framework combining organizational management, healthcare quality, patient satisfaction, and cost efficiency. Methods: An observational, descriptive, comparative study was conducted using data collected during 2018–2019 from two Romanian public hospitals with different organizational profiles: a multidisciplinary general hospital and a monospecialty hospital. Organizational, operational, financial, and clinical indicators were analyzed comparatively. Patient satisfaction was assessed in 184 hospitalized patients, including 130 from the general hospital and 54 from the monospecialty hospital, using a structured questionnaire with excellent internal consistency (Cronbach’s α = 0.92). Cost efficiency was estimated using Stochastic Frontier Analysis based on hospital expenditure, activity, resource utilization, case complexity, and quality-related variables. Results: Significant differences were identified between the hospitals in staff composition, bed occupancy, outpatient activity, case-mix complexity, surgical activity, healthcare quality, and financial performance. Patient satisfaction was generally high in both institutions, although several dimensions differed significantly, particularly overall satisfaction, waiting time, physician consultation, treatment received, and adherence to the prescribed medication schedule. The general hospital had a lower mean cost-inefficiency score than the monospecialty hospital (0.253 vs. 0.395), corresponding to higher estimated cost efficiency (0.747 vs. 0.605; p < 0.001). Conclusions: The proposed framework offers a comprehensive and practical approach to hospital performance assessment, and its application in two public hospitals provides a proof-of-concept demonstration of feasibility. Further multicenter studies are required for external validation and assessment of its generalizability across different hospital settings.