Resistive Random Access Memory (RRAM)-based FPGA architectures employ RRAMs not only as memories to store the configuration but embed them in the datapaths of programmable routing resources to propagate signals with improved performances. Sources of power consumption have been intensively studied for conventional Static Random Access Memories (SRAM)-based FPGAs. However, very limited works focused so far on studying the power characteristics of RRAM-based FPGAs. In this paper, we first analyze the power characteristics of RRAM-based multiplexer at circuit level and then use electrical simulations to study power consumption of RRAM-based FPGA architectures. Experimental results show that RRAM-based FPGAs achieve a Power-Delay Product reduced by 50% compared to SRAM-based FPGA at nominal voltage and 20% compared to near-Vt SRAM-based FPGA, respectively.