Thermodynamic analysis of various cycles (for single- or multi-generation systems) is a major topic on which lots of attention is paid in recent years. In such research activities, setting up an experimental rig is very time and money consuming, thus many of research works are conducted theoretically and the results are verified using the available data in literature. However, details of cycle modeling in component level has received little attention, albeit it has crucial effects on the obtained results from theoretical modeling and simulation. To demonstrate this issue in this paper, two different modeling approaches, which have been commonly used in previous literature to model the heat exchangers in thermodynamic cycles, are compared. To attain this goal, a biomass-fueled externally fired closed cycle gas turbine is proposed and its performance is compared with that of conventional open cycle gas turbine. To model the Intermediate Heat Exchanger (IHE), two approaches are considered: Approach (a): assuming a proper value for cold end temperature difference, and Approach (b): assuming a proper value for heat exchanger effectiveness. A comprehensive thermoeconomic analysis is conducted to evaluate the two considered systems’ performance via applying the two modeling approaches. The results revealed that, applying different modeling approaches brings about attaining conflicting outcomes, a conclusion which is not desirable from engineering perspective and reveals the crucial importance of applying appropriate modeling approach. It is found that, via applying approach (b) as the more rational approach, the closed cycle gas turbine yields a lower value of LCOE by 16.3% and a higher value of net output power by 13.5% than the conventional open cycle system.