This study evaluates the electrical, thermal and mechanical properties of various free-standing carbon nanomaterials to draw a holistic comparison for energy transport capabilities and possible lightning strike protection for aerospace. The tested materials include pristine carbon nanotube (CNT) buckpapers as well as CNT-polymer composites. The current carrying capacity (CCC) method provides the breakdown current density and the breakdown temperature, which was compared to the thermogravimetric analysis (TGA) results for each of the tested samples. For pristine CNT buckypaper samples, there was a positive correlation between the room-temperature electrical conductivity and the breakdown current density. CNT samples with high density, unidirectional nanotubes show superior conductivity and CCC results compared to randomly orientated CNT buckypaper. In addition, it was found that resin infiltrated CNT composites with polymers of high thermal stability exhibit higher breakdown current densities and greater electrical energy dissipation. Results from tensile testing revealed that the CCC of mechanically inferior CNT samples increased significantly when infiltrated with resin due to mechanical enhancement of the sample, resulting in better resistance against electrically induced thermal shock. Finally, it was noted that resin infiltration increased the breakdown temperature of the CNTs during the CCC testing.