I suppose this is obvious, but it recently struck me that a nice way to explain the advantage of markets is in terms of their distributed intelligence.
Two underlying premises are (a) that the world will undergo continual and in many ways unpredictable change and (b) that success is defined at least in part as the ability to adapt to and exploit those changes.
A market-based system consists of agents that spend much of their time looking for exploitable anomalies: inefficiencies, niches, arbitrage opportunities, and newly created needs. Those anomalies come into existence as a result of change. One can't predict where or when they will appear. The better a society/economy is at seeing and filling them, the more successful it will be.
Because a market-based system has eyes and intelligence everywhere looking for these opportunities it is likely to see them as quickly as possible. A centrally planned and controlled system simply cannot be that omniscient.
And in fact, one of the effects of the web and our increased interconnectedness is to amplify the property of being all-seeing and all-knowing. Increasingly, intelligence and perception are being connected in such a way that make it possible to see and exploit changes and opportunities even better and faster.