So, the first thing you have to understand is that the modern narrative taught in schools today that outlines the existence of a binary with Martin Luther King, Jr. on one side and Malcolm X on the other did not actually exist. Civil Rights as a whole involved a much more fluid link between violent and non-violent action. Proof of this can be found in Coming of Age in Mississippi by Anne Moody, in which she discusses her time in the Student Nonviolent Coordinating Committee (SNCC). SNCC was, as the name suggests, nonviolent, but members did have to resort to the threat of violence often to protect fellow members. So you cannot merely look at what Malcolm X did himself because he was a piece of a larger movement that is credited with achieving much more than any individual can be (I cannot find it right now, but there is actually a picture of King of Malcolm marching and leading thousands of people—thus, he was part of the tactic of visibility in the news media that helped the Civil Rights Movement achieve what it did). In my view, Malcolm X’s greatest achievement/contribution was the spread of his articulate thoughts. He was an incredibly intelligent man who helped to gain national and international visibility and interest for the Civil Rights Movement. One famous example was his Oxford Union Debate speech in which he defends, quite convincingly, extremism, although he lost the overall debate (https://www.youtube.com/watch?v=UMl4Na9Y2fE). One could say that through his visibility and outspokenness he gave rise to a number of people and organizations that are important to the history of Civil Rights. The best example of this is probably the Black Power movement, which was initially started by Stokely Carmichael, a former leader of SNCC. The Black Power movement was an extension of Malcolm’s rhetoric as it glorified and emphasized the strength, beauty and unity of African American communities. It was not that members of Black Power or followers of Malcolm did not believe in Martin Luther King or the effectiveness of nonviolent action, but that they were tired. It is hard to imagine the kind of psychological and physical abuse the member of SNCC had to endure, by comparison Black Power was a safe haven for people that no longer wanted to subject themselves to brutality, or the threat of brutality, and instead wanted to protect each other as a community.

Hey, so this is a little unorganized so apologies for that.

One important thing to consider here is that the popular narrative of MLK vs Malcolm is one largely advanced by a white Northern establishment; the former dealt with mostly Southern problems. It's not hard to imagine why, when faced with two civil rights icons, they would choose to favor the one who asks them to support a cause instead of one who accuses them of being active participants in racism. It's also worth considering that many, Malcolm included, believed that more militant strains of the black left made the white establishment more willing to work with MLK's ilk; a nonviolent leader gets a lot more done if the alternative is scarier.

I think that there is an argument to be made that Malcolm X was more a cultural figure than a political actor, and as such it's hard to measure his success in terms of laws, legislation, and other concrete advances. Moreover, he considered even the term "civil rights" to be a misnomer. As he stated in his Ballot-or-the-Bullet speech:

The common goal of 22 million Afro-Americans is respect as human beings, the God-given right to be a human being. Our common goal is to obtain the human rights that America has been denying us. We can never get civil rights in America until our human rights are first restored. We will never be recognized as citizens there until we are first recognized as humans.

MLK Jr's legacy is perhaps best understood in terms of legislation, coalitions, lawsuits, that sort of thing. For Malcolm, there was a sense that black America saw itself through the lens of white America, and acted accordingly - going into serious debt to keep up with fashions and to be able to brag about their jobs serving rich white people, straightening their hair, buying knock-off "white" products instead of keeping money in their communities, paying above market price for a house in a white neighborhood where they wouldn't be welcome. And because of his lack of a unifying, coherent political philosophy, it's easiest to quantify his impact culturally, in the fashions of natural hair and black-is-beautiful that emerged from his rhetoric, in the funk and hip-hop that drew inspiration from him, in the adoption of African and African-sounding names and fashions in black communities.

In his words:

Who taught you to hate the texture of your hair? Who taught you to hate the color of your skin? Who taught you to hate the shape of your nose and the shape of your lips? Who taught you to hate yourself from the top of your head to the soles of your feet? Who taught you to hate your own kind?

It's also crucial to understand that for blacks outside of the South, the struggle for "civil rights" was a different struggle altogether. The South had clearly codified laws that could be dismantled; Northern segregation was a much more subtle and tangled mess of disadvantages (including even infrastructural segregation, like placement of highways and bridge clearances built specifically to disadvantage black people) that have historically proven much more difficult to dismantle. Northern blacks already had the vote, they already mostly (technically speaking) had desegregated facilities, and yet they were still terrorized, disadvantaged, and largely barred from the same economic advantages that white citizens had. So "civil rights" was not the most applicable term, in Malcolm's view, and an ethos of nonviolence seemed absurd to a people who found themselves so frequently the victims of state and state-sanctioned violence. A big part of his legacy is in articulating this; one of the reasons he has not had the same positive reputation that MLK has among whites is that he was quick to point out that the same white liberals who were quick to look down on Southern racists were participants in, and agents of, another type of segregation in the North.

Malcolm's legacy is more in the values he preached and in the life experience he related than in any legislation he didn't get passed, and his preaching of those values had impact because they didn't come from a sense of church moralizing (even though he was religious) or someone who was always upstanding; he was a former hustler, burglar, and drug dealer/user. And here he was preaching education, getting off of drugs, recycling money within black communities, starting and supporting black businesses, and taking pride in one's race. That last point can sound off-putting, but it's important to take it in historical context - black physical beauty had been judged in the USA according to how white a black person's features were, and here was a leader preaching the value of natural hair and making a point of how perverse it was to idolize features that were most likely the result of rape and slavery.

(Taken in a bundle with his insistence that blacks use their Second-Amendment rights for self-defense and his negative feelings towards government hand-outs, it's somewhat ironic that he was and is so vilified by the right in the US, since so many of his values match with the values the GOP has historically voiced when talking about black issues. But that's an issue for another day and a whole piece about dog whistles).

Looking at many Malcolm X pieces penned by black authors, the theme that emerges is less political and more personal - Ta Nehisi-Coates in "The Legacy of Malcolm X" wrote about his and his mother's sense of identity, their adoption of natural hair, and the various narratives for a black life they Malcolm's story made possible for them. Spike Lee's biopic was less a political film and more a personal journey, less about a movement and more about one man's personal evolution, his transformation from a hustler whose family had been torn apart by racism to a self-actualized, self-educated, prideful black man who commanded authority and respect.

Malcolm X's autobiography consistently came back to the theme of wasted talent - of him having a talent for law, but not becoming a lawyer because of white teachers discouraging him. Of another hustler who could've been a great engineer with his knack for numbers, had he been white. Malcolm's autobiography - and his frankness about where he came from and how he and his views changed - gave a narrative for what a black man COULD be, and coupled with his agenda of black self-determination arguably inspired a whole generation of black people to take advantage of expanded rights and opportunities and to generate wealth, business, and art.

I hope this is helpful.

Major citation in this case is the Autobiography of Malcolm X, which is an admittedly biased source.