As the world shift towards sustainable energy solutions, solid oxide fuel cells (SOFCs) using non-carbon fuels like ammonia and hydrogen emerge as promising pathways to produce clean energy and enhance conversion efficiency. However, current implementations encounter challenges such as nitriding effects from direct ammonia injection to the stack, overestimated benefits of anode off-gas (AOG) recirculation, and a sole focus on electrical efficiency that overlooks the thermal advantages of SOFCs. This study addresses these gaps through a comprehensive multi-objective optimization of SOFC systems fueled by ammonia and hydrogen, assessing their efficiency, fuel utilization, and heat exergy. The research translates material phenomena into mathematical constraints and quantifies the effects of control variables through systematic parameter variation. Results indicate that ammonia-fueled SOFC systems slightly outperform hydrogen, achieving an electrical efficiency of about 65% compared to 62% for hydrogen systems, although hydrogen demonstrates superior fuel utilization and exergy efficiency. Optimal AOG recirculation and NH3 cracking fraction that do not compromise stack lifetime and stay in the safe operating zone of nitriding are identified. It also challenges the assumptions that a higher AOG recirculation can benefit performance, suggesting that more extensive AOG recirculation might not always enhance it. Soft sensors are provided to predict system's performance and enable proactive adjustments to facilitate industrial applications where some parameters, such as high-temperature stack's pressure drop, are costly or difficult to measure. This study significantly advances the practical deployment of SOFC technologies, enhancing their feasibility for sustainable energy development.