Energy storage offers the flexibility needed to integrate renewable generation into electricity systems. One decentralized option is to install battery packs in homes and offices. Yet storage owners might operate their device autonomously to minimize their own electricity costs, but this could be inefficient from a wider electricity system perspective. Using a novel agent-based power system model, ESMA, we explore the economic trade-offs of aggregator-led (centralized) and consumer-led (decentralized) coordination in the UK over the period 2015-2040. We consider the deployment of storage in the domestic, commercial and industrial sectors. Centralized scheduling leads to the lowest power system cost, reducing mean electricity prices by up to 7% relative to decentralized scheduling. This could avoid annual bill increases of up to 407 m pound/year and could decrease electricity price volatility by up to 60%, depending on the installed storage capacity on the grid. We show that aggregators could reduce the disparity between private and system value by financially incentivizing consumers to give up control of their storage resource in order to use it more efficiently for the benefit of the wider electricity system.