In this current study, the energy, exergy, economic, and environmental efficiency of an integrated solid oxide fuel cell (SOFC) with two proposed waste heat recovery cycles - an organic Rankine cycle (ORC) and a supercritical carbon dioxide Brayton cycle (sCO₂) was investigated. The SOFC model used in the analysis was detailed and included electrochemical equations along with expressions for activation, ohmic, and concentration losses derived from it and was validated against reference experimental data. Then a systematic energy and exergy analysis of the complete system was performed to identify the optimum cycle in terms of efficiency and SWOT evaluation. The supercritical carbon dioxide Brayton cycle was then optimized multi-objectively with the Grey Wolf Optimizer (GWO) algorithm for maximum power and minimum destruction of exergy. The results indicated that an increase in the current density from 0.4 to 1 A/cm² reduced the cell voltage from 0.88 to 0.63 V, while the recovered heat increased from 12 to 25 kW. At the optimal position from the GWO, the energy efficiency, net system power, current density, and total rate of exergy destruction were 0.875 A/cm², 501 kW, 53.74%, and approximately 377.23 kW, respectively. The comparison between the two configurations showed that the energy efficiency of the SOFC–sCO₂ system was greater than that of the stand-alone SOFC by more than 24%. In addition, incorporation of the waste heat recovery system into the SOFC–sCO₂ system reduced the same CO₂ emissions by 39.21% relative to the independent SOFC system.