Improving the energy efficiency of data center has become a research focus in recent years. Previous works commonly adopted the inlet temperature constraint to optimize the thermal environment in the data center. However, the inlet temperature-aware method cannot prevent the servers from over-cooling. To cope with this issue, we propose a thermal-aware workload allocation strategy with respect to the chip temperature constraint. In this paper, we conducted a comparative evaluation of the performance between the chip and inlet temperature-aware workload allocation strategies. The workload allocation strategies adopt a POD-based heat recirculation model to characterize the thermal environment in data center. The contribution of the temperature-dependent leakage power to server power consumption is also considered. We adopted a sample data center under constant-flow and variable-flow cooling air supply to evaluate the performance of these two different workload allocation strategies. The comparison results show that the chip temperature-aware workload allocation strategy prevents the servers from over-cooling and significantly improves the energy efficiency of data center, especially for the case of variable-flow cooling air supply.