Carbon nanomaterials show great promise for a wide range of applications due to their excellent physicochemical and electrical properties. Since their discovery, the state-of-the-art has expanded the scope of their application from scientific curiosity to impactful solutions. Due to their tunability, carbon nanomaterials can be processed into a wide range of formulations and significant scope exists to couple carbon structures to electronic and electrochemical applications. In this paper, the electrochemical performance of various types of CNT films, which differ by the number of walls, diameter, chirality and surface chemistry is presented. Especially, chirality-sorted (6,5)- and (7,6)-based CNT films are shown to possess a high charge storage capacity (up to 621.91 mC cm2), areal capacitance (262 mF cm2), significantly increased effective surface area and advantageous charge/discharge characteristics without addition of any external species, and outperform many other high capacity materials reported in the literature. The results suggest that the control over the CNT structure can lead to the manufacture of macroscopic CNT devices precisely tailored for a wide range of applications, with the focus on energy storage devices and supercapacitors. The sorted CNT macroassemblies show great potential for energy storage technologies to come from R&D laboratories into real life.