The modern consciousness regarding the Civil Rights Movement is one where Dr. King is located at its center.  Dr. King is the fulcrum point from which all else in the movement rotates.  Dr. King can be seen as more significant than Malcolm X because of his ability to reach across racial lines and construct the Civil Rights Movement as a human issue.  

Prior to Dr. King, White Americans had viewed the issue of Civil Rights as a political issue, one where states rights and issues of federalism trumped all.  Yet, Dr. King placed the Civil Rights debate in moralistic terms.  Invoking Gandhian precepts, Dr. King transformed the discussion into one where human notions of the good were posited. When Dr. King speaks of his "dream," one sees how the issue of Civil Rights is a moral and spiritual issue, a construction where the ability for the individual to envision a better life for themselves and their loved ones is a part of what racial equality means.  Dr. King has to be seen as more significant than Malcolm X because of his ability to transform the dialogue into one that embraced more people and helped to change minds about the issue of Civil Rights.

Malcolm X holds much in way of significance to the Civil Rights discourse and movement.  He occupies a central role in articulating a narrative for people of color and speaking to them about the conditions in which they live.  Yet, Dr. King is more significant to the historical consciousness of the Civil Rights Movement because of how he was able to transform how people saw racial injustice and prejudice.  Through transcending the issue of race into a humanist frame of reference, Dr. King proved to be more significant to the concept of Civil Rights.

First, we must realize that there is no objective way to say which man was more significant.  A person could argue that Malcolm X was more significant.  However, most people would say that King was more significant and that there were two main reasons for this.

First, we can say King was more significant because he was more involved in the movement that won civil rights for African Americans.  King was the person who was most closely connected to the Civil Rights Movement.  It was he who spoke at the March on Washington.  It was he who helped to organize the Montgomery Bus Boycott.  This meant that he, unlike Malcolm X, was very much involved in the most significant changes of the 1960s.

Second, we can say that King was more significant because he was less militant that Malcolm X.  King was an inclusionist, integrationist activist.  He did not espouse the idea of black power or of black nationalism.  This made him much more acceptable to the white majority in the United States.  Because he was more acceptable to them, he was more able to accomplish his goals than Malcolm X was.

Why was Malcolm X a better civil rights leader than MLK Jr.?

Malcolm X was not a "better civil rights leader" than Martin Luther King, Jr. but a different one; though, toward the end of their lives their views began to converge.

Malcolm X was a controversial figure among the white establishment and also mainstream civil rights leaders, particularly those in the NAACP. His advocacy of black separatism, encouraged by the teachings of the Nation of Islam, fostered a blanket indictment of all white people, even those who attempted to be allies, as evil. On the other hand, this view also encouraged self-sufficiency and self-determination—values that Malcolm X maintained when he left the Nation of Islam and formed the Organization of Afro-American Unity in 1964.

Dr. King was also a controversial figure. Whites resented his refusal to slow the progress of integration and some blacks—particularly radical black nationalists, such as Malcolm X—viewed him as an "Uncle Tom" who foolishly sought to make peace with a lethal enemy.

Both King and Malcolm X sought for black people to have more equity and freedom in American life, and both focused their efforts particularly on elevating the plight of the poor. Malcolm X's career as a civil rights leader was based in impoverished Harlem. Dr. King worked not only on integration efforts but also to organize low-wage workers. He traveled to Memphis, Tennessee in April 1968 to help organize sanitation workers. For both men, poverty and racism were interrelated and required equal redress.

Why was MLK a more essential civil rights leader than Malcolm X?

Malcolm X was more interested in a separate nation for Blacks rather than Civil Rights.  His famous "by any means necessary" speech in which he advocated the killing of Caucasians to obtain the goals of his group certainly was not a call to unite the nation.  His radical ideals of black identity, integrity, and independence challenged King's dream of equal opportunity. 

Having a background as a youth that was less than stellar--street hustler, drug dealer, and leader of a gang of thieves in Roxbury and Harlem, imprisoned for robbery from 1946-1952, joining the Nation of Islam and changing his surname Little to X as a rejection of white slave names--did not lend him the credibility with other races that the Reverend Martin Luther King had, either.

Sources:

http://www.biography.com/articles/Malcolm-X-9396195?part=1

Why was MLK a more essential civil rights leader than Malcolm X?

The previous post's thoughts on whether or not "essential" is the most accurate descriptor is a valid one.  I think that Dr. King's primary message was something that allowed more Americans to accept the plausibility and need for Civil Rights for African- Americans.  Dr. King's manner of framing the movement as something that was driven by an acknowledgement of human rights, making the political struggle a moral one.  For example, in the "I Have a Dream" speech, civil rights for African- Americans was seen in a moral light, an ethical and spiritual responsibility for all to acknowledge.  Certainly, other leaders argued the same elements, but Dr. King was seen as the spiritual figurehead for the movement, the individual with whom so much morality was associated.  In this light, he was able to bring moderate and liberal white Americans to a struggle that was largely seen as solely a black problem.

That being said, I don't think one can discount the impact of nationalistic leaders like Malcolm X.  While his vision caused a great deal of fear and consternation in the same people that felt comfortable with King's, I think that this was deliberate.  Malcolm X's stance and deliberate calls helped to bring to light the idea that if white Americans were not comfortable with Dr. King's solutions, there were other approaches that might be more threatening than anything else.  I think that later on in his philosophy Malcolm X understood that one of his functions was to get more people to embrace King's vision specifically because what he was articulating was deemed as so "radical" for the time period.  In the oddest of ways, acting as an occasional foil helped to bring the two men closer together and show alliances while others sought to create division.

Why was MLK a more essential civil rights leader than Malcolm X?

I guess I am not sure what you mean by essential, but he was a more successful civil rights leader because of his ability to appeal to white Americans.

Although the Civil Rights Movement was driven by the efforts of black people, the movement could only succeed with white support.  This is a basic truth in a country that, in those days, was more than 80% white.

Martin Luther King appealed to moderate whites.  His message of nonviolence and universal brotherhood was an attractive message.  He was a Christian minister, educated and middle class.

Malcolm X was an ex-convict who was, especially early on, anti-white.  He was a black nationalist, uneducated, and Muslim.

Because of their different backgrounds and different attitudes, King could be much more persuasive to white audiences.