Two categories of thermoelectric systems, i.e. thermoelectric active cooling (TAC) and thermoelectric self-cooling (TSC), were broadly applied for electronic cooling. Energy efficiency maximization and entropy generation minimization will be simultaneously achieved for both thermoelectric systems. Thermodynamic models of TAC and TSC systems are established to clarify the effects of main influencing parameters (i.e., applied current, thermal conductance in hot and cold ends) on the energy and entropy performances. Subsequently, under the situation of electronic cooling with constant material properties, a comprehensive performance comparison between TAC and TSC has been conducted, including decision targets, irreversible characteristics and environmental impacts. Furthermore, in order to improve the heat dissipation potential, the effects of material properties on the system performance are also sensitively identified for both TAC and TSC systems. For both systems, internal irreversibility is more pronounced than external one. Numerical results demonstrated that system efficiency of TAC could be higher than that of TSC; the operating mode for TAC could be completely switched to that for TSC when the input power was turned into zero. Present investigation could give suitable guidelines for thermoelectric systems applied for electronic cooling.