It is possible to argue this in two ways. It is possible to say that a market economy would handle this situation best, but it is also possible to say that a command economy (the more totalitarian the better) would be more efficient.
It is possible to argue that a command economy can move more quickly to deal with the effects of a major disaster. In such an economy, the government is in control and can simply order resources to the affected area. The government will not have to waste time with things like putting out contracts for services. It simply tells people to go and work on the recovery efforts and they will go. This, arguably, would allow a command economy to be the most effective at dealing with a major disaster.
However, it is also possible to argue that a market economy is the best system for dealing with disaster. The argument here is that governments simply do not work efficiently, regardless of how much power they have. The various people in government do not have much of an incentive to work their hardest to make the recovery happen. By contrast, firms in a market economy would have a motive (the profit motive) to work quickly and efficiently. They would also tend to have the expertise needed to accomplish the task. This is, for example, why some people argue that large stores like WalMart, Lowe’s, and Home Depot were better able to get supplies to places that were hit by Hurricane Sandy than the government was.