Multifunctional structural power composites, which combine mechanical load-bearing and electrochemical energy storage, will transform electric vehicle design. This work focuses on structural supercapacitors, based on carbon aerogel-modified carbon fibre electrodes with copper current collectors. In common with many structural power embodiments, scale-up of these devices is currently limited by large internal resistances and the mass associated with current collection. There is a trade-off between the overall resistive power loss and the additional mass for the current collector material. However, in these devices, mechanical integrity is provided by the structural electrodes, allowing a range of collector designs to be considered. Using finite element simulations, these current collection strategies are explored quantitatively across a range of design space variables. The key conductivity parameters were measured experimentally, using the best existing materials, to inform direct current conduction simulations of the electrode/current collector assembly. For the present device configuration, the performance trade-off is governed by the area of the current collector. The most effective near-term strategy for power loss mitigation lies in reducing the contact resistance; however, improvements can also be obtained by modifying the collector geometry. The findings of this paper can be generalised to other structural power composites and monofunctional energy storage devices, which are relevant in many mass-sensitive electrochemical applications.