think is stronger.

On the one hand, you can say that Brown was more important. This decision did at least two things.  First, it ended segregation in education. This was very important in and of itself because it allowed African American children to go to school with whites.  This made our country more just and it also increased the opportunities open to black students.  Secondly, the case also implied that other kinds of segregation were illegal.  If it were not for Brown, African Americans might not have been so confident that they could overturn the Jim Crow laws that remained.  If it were not for Brown, whites in the North might not have felt that the protestors of the Civil Rights Movement had the law on their side.  In short, this court case unlocked the door for the Civil Rights Movement.

On the other hand, you can say that the bus boycott represented black people actually pushing through the door that Brown had unlocked.  Brown gave African Americans the opportunity, but the bus boycott was the first instance of blacks actually engaging in nonviolent actions to take that opportunity.  We can argue that the Court case by itself would not have done enough to end racial discrimination.  In order to end discrimination, an actual movement of the people was needed.  It was this movement that ended up leading to the Civil Rights Act of 1964 and the Voting Rights Act of 1965.  These laws had a much greater impact than the Brown decision did.  So, from this point of view, the bus boycott was much more important because it was the start of a massive movement by the people to claim rights.  Such a movement is much more important than a single Supreme Court case.  A large popular movement is able to put pressure on the government to change the laws and that is what the Civil Rights Movement did.  The Montgomery Bus Boycott, then, is more important because it started that movement.

Which of these arguments makes more sense to you?

This question, of course, is open to interpretation, but I would argue that the Supreme Court's decision in Brown v. Board of Education was more significant. While the Montgomery Bus Boycott catapulted Martin Luther King, Jr. to the national consciousness and illustrated the possibilities of nonviolent protest, the sit-ins at Greensboro five years later were probably more significant in terms of sparking a nationwide movement, especially among youth. Brown v. Board, on the other hand, by ruling segregation in public schools unconstitutional, was a major step toward weakening the legal basis for Jim Crow. Southern segregationists quickly grasped the significance of the decision, many calling for "massive resistance" to federally-mandated integration. It was, in fact, this resistance that led to the first significant use of federal power to enforce integration, in Little Rock, Arkansas, in 1957. Brown v. Board did not lead to immediate, or even rapid, integration. But we can see with the benefit of hindsight that it did create a crisis for the institutions that allowed segregation in the South, and it began a process by which the federal government would intervene to enforce the protections afforded by the Fourteenth Amendment in a number of different contexts. Of course, the government was spurred on by the crises created by the scale of the movement in the 1960s, and by the ferocity of segregationists' responses, but Brown v. Board nudged the constitutional balance away from Jim Crow and toward equality.