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.
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.
Malcolm X isn't neccesarily more significant than Martin Luther King Jr., it is just they did different things for Black rights. Malcom X preached for black rights, but he wanted violence, which caused the rise of the black power movement. Although, later on he became a muslim, he advocated for peace, and was later assinated in 1965. Martin Luther King Jr. was very peaceful and preached for black rights, but through non-violence. Such as marches and speeches to help unify the people to accquire rights through peace. They both had different ways of preaching, but they preached for the same reason, black rights. Dr.Martin Luther King Jr's method was more effective, and everyone remebers his I have a dream speech, which is why we remember him more, over Malcolm X.