What most people say is that the market economy is the best at giving the people what they want, but that it tends to be "unfair." By contrast, a command economy is generally said to have the ability to be more fair and to be easier to change when needed. However, this sort of economy is not as good at giving the people what they want.
Market economies give people the widest variety of the highest possible quality of product at the lowest possible price. They also allow people to make their own choices. But market economies allow some people to be rich and others to be poor, often without good reason.
Command economies can be fairer because the government can take from the rich and give to the poor if it wants to. (This does not always happen.) They can change themselves more rapidly. China is a case in point -- their government has recently ordered some factories to close because they are not energy effficient enough. This is not possible in a market economy. However, China (and command economies in general) does not really give people the freedom to act as they wish.
We can think of two opposing approaches that a society can adopt to manage its economic system or to answer the economic question of how what and for whom to produce the goods and services using the scarce resources of the society. These are called market economy and command economy. These two system represents two extremes along a continuum representing mix of the two approaches in different proportions.
In a market economy individuals and private firms make the major economic decisions with a view to maximize their rewards and benefits. Thus firms decide on the variety and quantity of goods to produce on the basis of what they expect to yield them maximum profit. The consumer decide to buy and use the goods and services that they expect to yield maximum satisfaction or benefit to them. In command economy all major economic decision about production and distribution are taken by the government.
The biggest advantage of market economy is that it is very simple and requires no expertise or elaborate infrastructure to implement. It is a system that is expected to operate automatically. Also this system is supposed to provide greatest incentive to individuals to make best use of their resources achieving high levels of effectiveness and efficiency. However, the market system rarely operates as efficiently or smoothly as it is expected in theory. Many imperfections exist in practical operations of market mechanism due to reasons such as imperfect flow of information and barriers entry and exit into specific industries. All these result in some individuals making excessive profits at the expense of others. Such imperfections of market economy also tends to affect efficiency.
The command economy is justified on the logic that the government can decide what is in the best interest of the society as a whole and then ensure that the economy is run accordingly. This logic appears very attractive when it is assumed that the government is composed of representatives of the people and is fully committed to the general good of the people. However their are many problems. First and foremost problem is that it is not possible to determine with any degree of certainty what actions or decisions will maximize the good of the people. In addition we cannot take for granted that people responsible for decision making and implementation in the government are always and fully committed to the good of the people. Also implementation of the centralised decision requires a mechanism that becomes too cumbersome involving heavy costs and delays. A command economy which thus becomes ineffective is also not able to motivate the people to act in the interest of the common good of the society.