This article compares the performance of two energy storage technologies, namely supercapacitors and Li-ion batteries, in the context of Direct Wave Energy Converters (DWEC). Both the sizing and management of an Energy Storage System (ESS) are described, and the SEAREV project has been used as an example. The main objective is to compare the two technologies on the basis of their life cycle cost. The ESS is necessary for grid integration due to the flicker constraint, which is not being satisfied without storage. The rule-based energy management approach introduced herein depends on the State of Energy of this ESS as well as the power produced by the DWEC. This management strategy has been optimized for each size in order to reduce aging speed while strictly respecting the flicker criterion. The final design is expected to minimize total system cost, i.e. the sum of investment cost and operating cost (losses and replacements). The aging models applied take into account temperature and cycling effect in order to estimate this replacement cost. Such an optimization routine is especially critical for offshore systems like Direct Wave Energy Converters, which require both cost reduction and high reliability.