Although nanocarbon-based nanofillers have been widely used to improve the energy-storing and sensing functions of porous materials, the comparison of the effects of different nanocarbon-based fillers on the capacitive and flexible sensing properties of nanocarbon-based porous sponge composite supercapacitor electrodes by combining a carbon nanotube, graphene, and graphene oxide with porous sponge is incomplete. The specific capacitance of carbon nanotube-based electrodes is 20.1 F/g. The specific capacitance of graphene-based electrodes is 26.7 F/g. The specific capacitance of graphene oxide-based electrodes is 78.1 F/g, and the capacity retention rate is 92.99% under 20000 charge-discharge cycles. Under a bending load of 180°, the capacitance retention rate of graphene oxide sponge composite electrodes is 67.46%, which indicates that the prepared electrodes of supercapacitor have the advantages of high capacitance and good flexibility at the same time. To demonstrate their performance, an array of three graphene oxide supercapacitors in series was constructed, which could light up a red light-emitting diode (LED). The tensile strength of carbon nanotube sponge composite electrodes is 0.267 MPa, and the tensile linearity is 0.0169. The experimental results show that graphene oxide-based sponge composite supercapacitor electrodes have the best capacitance performance and carbon nanotube sponge composites have the most potential as a flexible sensor.