A typical operating condition of storage batteries requires to deliver and absorb small currents in large intervals of time, in order of minutes or hours. However, in the last years lithium batteries have been more and more considered in “power oriented” applications, in which they are required to manage large currents in short intervals of time, typically a few seconds or tens of seconds. Unfortunately, very limited information about this kind of usage is available in literature, in terms of battery performance and aging. Therefore, the paper focuses firstly on the experimental evaluation of performance of high power and super high power lithium batteries also in comparison to other power oriented storage systems adequate for use onboard hybrid vehicles, such as supercapacitors (SCs). The evaluation has been performed through experimental tests. Results have shown that these batteries are able to guarantee significant performance, even higher than data declared by manufacturer, with slight over-temperature. Then, for high power lithium batteries aging is discussed, when they are subjected to shallow-depth charge/discharge cycles. The aim is to evaluate if the battery life corresponding to such micro-cycles can reach several hundreds of thousands that are required for applications such as hybrid vehicles and hybrid stationary generation systems. Also in this case experimental tests able to prove it have been executed. They have shown a substantially unaltered capacity fade during the execution of hundreds of thousands of micro-cycles, thus confirming the vocation of these devices for power-oriented applications.