This is a bit of an opinion question, but I believe properly implemented they serve slightly different purposes. The minimum wage is a price and wage stabilizer. The EITC is a poverty reduction program. So it is improper to try to consider an equivalent of one to the other. I will explain their benefits as they are enacted, so you will see why there are two programs.
The minimum wage was implemented during the Great Depression to prevent the downward spiral of wages and prices, a process known as deflation. It does this by acting as a price floor.
An example of a price floor is minimum wage laws; in this case, employees are the suppliers of labor and the company is the consumer. When the minimum wage is set higher than the equilibrium market price for unskilled labor, unemployment is created (more people are looking for jobs than there are jobs available). A minimum wage above the equilibrium wage would induce employers to hire fewer workers as well as allow more people to enter the labor market, the result is a surplus in the amount of labor available. The equilibrium wage for a worker would be dependent upon the worker's skill sets along with market conditions.
Therefore, it is normally set at or below the range employers pay their cheapest employees to prevent unemployment. It is not very useful for poverty reduction during times of economic growth due to this effect. Yet in a recession, when there is deflation, it is a great stabilizer, so it is a good policy, according to Keynesian economics. Setting a price floor may have knock-on effects for other workers making above the minimum wage as well. Certainly in a severely deflationary environment, it prevents the workers making above minimum wage from making less than minimum wage, which could happen. During the Great Depression wages fell by 25%.
First, he argued that it is not real but nominal wages that are set in negotiations between employers and workers, as opposed to a barter relationship. Second, nominal wage cuts would be difficult to put into effect because of laws and wage contracts. Even classical economists admitted that these exist; unlike Keynes, they advocated abolishing minimum wages, unions, and long-term contracts, increasing labour market flexibility. However, to Keynes, people will resist nominal wage reductions, even without unions, until they see other wages falling and a general fall of prices.
Keynes rejected the idea that cutting wages would cure recessions. He examined the explanations for this idea and found them all faulty. He also considered the most likely consequences of cutting wages in recessions, under various different circumstances. He concluded that such wage cutting would be more likely to make recessions worse rather than better.
Further, if wages and prices were falling, people would start to expect them to fall. This could make the economy spiral downward as those who had money would simply wait as falling prices made it more valuable – rather than spending. As Irving Fisher argued in 1933, in his Debt-Deflation Theory of Great Depressions, deflation (falling prices) can make a depression deeper as falling prices and wages made pre-existing nominal debts more valuable in real terms.
It has a few other effects, we consider positive at its current low rate: it prevents abuse of new immigrants or or others who are not very informed of "average" wages; it causes employers to consider spending more on investments than manual labor, which often leads to better working conditions and combined with business-friendly policies, leads to innovative, new products; it leads to employers hiring older workers over younger workers. Democratic socialist nations of Europe, such as Germany have more innovative manufacturing sectors due to the high cost of labor, so it reasons that a slightly higher cost of labor induces some innovation in the US. The last reason can be controversial, since its good for young workers to get job experience, but education including college is increasingly important in the modern world.
The EITC in contrast is properly used as a poverty reduction program. It can't be used to stabilize prices, though since it redistributes tax money, rather than acting on the employers or prices themselves. Many who work low wage jobs don't make enough money to pay their bills and have a good standard of living, but because they work they don't qualify for other welfare programs. Using the tax system to distribute money is usually much more efficient than using welfare programs, such as food stamps. According to the Center for Budget and Policy Priorities, administrative overhead for poverty reduction programs range from 1-10% of program cost. EITC overhead, the lowest cited, is less than 1%. Food stamps is about 10%.
It also encourages work, since you must be working to get it. This was a major idea behind Bill Clintons welfare reforms of the 1990s. "EITC benefits were $49.5 billion and "revenue protected" was $3.2 billion." Compared to other programs this a rather small program: SNAP costs in 2010 totaled $68.4 billion, $270 billion for Medicare (so its a 1/5th the size of a large program). Money spent on government programs is diverted from other purposes, so it can be a drag on economic activity especially if the amount is large through the process of malinvestment, according to Austrian economics.
Malinvestment is an investment in wrong lines of production which leads to capital losses.
Malinvestment results from the inability of investors to foresee correctly, at the time of investment, either the future pattern of consumer demand, or the future availability of more efficient means for satisfying consumer demand. Malinvestment is always the result of the inability of human beings to foresee future conditions correctly. However, such errors are most frequently compounded by the illusions created by undetected inflation.1
Personally I don't think that's too much of a problem here, especially since the money goes back into the consumer economy-rather than tied up into less than useful large infrastructure projects, military, large programs like Medicare ect. which cause distortions and economic dependence by hundreds of thousands of workers and businesses due to their size.