Advanced supercapacitors have great potential to transform how we store and utilize energy, leading to more efficient and sustainable energy systems. This study reveals the structural features influencing the interfacial thermal transport and electrical performances of supercapacitors using the constant potential and constant charge molecular dynamics simulation techniques. Thermal and electrical properties were calculated for graphene/carbon nanotube (CNT) composite electrodes and ionic liquid electrolytes with different nanotube diameters, numbers, layers, and alignments of the nanotubes. The effect of the application of a constant potential on the Kapitza resistance is determined for the first time. The vertically aligned CNT structures exhibited higher electrical performance, while the horizontal arrangement showed better thermal performance. Optimum electrode configurations were identified by considering thermal and electrical performances along with other design factors, such as structural stability, ease of manufacturing, and scalability. After considering all these factors, the horizontally stacked multilayer CNT arrangement emerged as the optimal electrode structure. The insights gained from this study aid in comprehending the effects of variations in the electrode structure, thereby enabling efficient supercapacitor electrode design.