With the establishment of the internet of things (IoT) and the rapid development of advanced microsystems, there is a growing demand to develop electrochemical capacitors (ECs) to replace bulky electrolytic capacitors on circuit boards for AC line filtering, and as a storage unit in energy autonomous systems. For this purpose, ECs must be capable of handling sufficiently high signal frequencies, display minimum energy loss through self-discharge and leakage current as well as maintaining an adequate capacitance. Here, we demonstrate ECs based on mechanically flexible, covalently bonded graphite/vertically aligned carbon nanotubes (graphite/VACNTs) hybrid materials. The ECs employing a KOH electrolyte exhibit a phase angle of -84.8 degrees, an areal capacitance of 1.38 mF cm(-2) and a volumetric capacitance (device level) of 345 mF cm(-3) at 120 Hz, which is among the highest values for carbon based high frequency ECs. Additionally, the performance as a storage EC for miniaturized systems is evaluated. We demonstrate capacitive charging/discharging at mu A current with a gel electrolyte, and sub-mu A leakage current reached within 50 s, and 100 nA level equilibrium leakage within 100 sat 2.0 V floating with an ionic liquid electrolyte.