Gas turbine cogeneration systems, operated under the Brayton cycle, are considered a beneficial solution among all biomass-fueled technologies, which are of interest nowadays. The system configuration with an external combustion chamber and heat regeneration, able to utilize low-grade alternative fuels while providing high energy generation efficiency, meets the main goals of the green transition and energy security, contributing to sustainability and lowering fuel consumption. Nevertheless, efforts are still being undertaken to improve such a system's performance in terms of efficiency and profitability. The sCO2 Brayton cycle, owing to the specific parameters of carbon dioxide at the near-critical and supercritical state, which allow for reducing the compression work, offers significantly improved system efficiency and increased net power output compared to the air Brayton cycle at the moderate turbine inlet temperatures. At the same time, sCO2 Brayton cycle units feature a more compact design, due to which the capital cost per unit of power can be reduced. This follows basically from smaller dimensions, up to four times, of turbomachinery, even though they require the use of more advanced, high-pressure-resistant materials. On the other hand, high operating pressures and temperatures require the use of more advanced technologies for a heat exchanger that serves as a recuperator to heat the working fluid directed to the turbine with the generated exhaust gases. This makes this component the main one in the system capital cost, accounting for as much as 50% of it. In the paper, an sCO2 Brayton cycle with heat recovery, indirectly fired by gaseous fuel, is considered, while focusing on the available technological solutions for the heat recuperator. Various heat exchanger designs are discussed in terms of their advantages and disadvantages for their potential application in the studied system, including pressure loss and manufacturing costs. The size of a heat exchanger for the selected cycle operating parameters will be determined and, further, compared with the size of a heat exchanger of a regenerative air Brayton cycle.