Wind power fluctuations are typical of small size wind farms and may be a limiting factor in isolated small-size systems. An electric storage can be used to mitigate these fluctuations and enable the use of wind energy to provide energy to remote communities or microgrids. This study compares the performance of Li-Ion batteries and flywheels in abating the ramp rates of the power produced by a wind turbine. Production data was generated from actual wind measurements over one year. The capability of ramp abatement by varying storage capacity, power rating and ramp rate thresholds was investigated. The storage technologies were compared from the technical and economic point of views by means of a multi-objective optimization approach that showed the optimal trade-off between abatement capability and costs. The costs of storage periodic replacement, due to the degradation induced by a cycling operation, was also estimated. Results suggest that the abetment of wind power ramps up to 80% can be done at a relatively low price (between 5 and 10 k€). In this case flywheels outperform batteries in term of cost. If a higher abatement effectiveness is required (around 90%) the storage cost quickly increases. In this case the battery outperforms the flywheel and provide the same performance at much lower cost. If strict requirements are assumed, i.e. maximum permitted fluctuations are lower than 5% of turbine rated power, an abatement effectiveness up to 95% is achievable, but the cost may be as high as 25 k€ per year. Otherwise, in case of a maximum permitted fluctuation lower than 10%, abatement effectiveness over 92% is hardly achieved (the cost is over 30 k€ per year). For abatements around 90%, an annual cost between 15 and 20 k€ may be found using batteries rather than flywheels.