Brazilian jiu jitsu fighters have challenged and fought boxers on many occasions, beginning with Helio Gracie's defeat of Antonio Portugal in 1932. Many of these challenges have simply been declined or ignored by professional boxers, but the debate still goes on. Mixed martial arts events are one of the only venues where it is possible to directly compare these very different fighting styles.
Helio Gracie and Boxing
Brazilian jiu jitsu established its formidable reputation through challenge matches in Brazil, many of which were "vale tudo," a Portugese phrase meaning "anything goes." Considering that boxing is entirely based on strikes while Brazilian jiu jitsu is mostly ground-fighting, a vale tudo match would seem to be the only way to compare the arts. A Brazilian jiu jitsu fighter would not be allowed to use of most of his techniques in a pure boxing match, and vice versa. In a match where anything goes, both fighters would be able to apply their techniques. In a vale tudo fight between Brazilian jiu jitsu instructor Gracie and boxer Portugal in 1932, Gracie prevailed in just 30 seconds. He went on to challenge famous boxers such as Primo Carnera and Joe Louis, but they were unwilling to fight him.
The Issue of Range
Boxing matches occur primarily at striking range, and boxers are not allowed to throw each other. Because of this restriction, boxers do not ordinarily train against takedowns and do not need to worry about preventing an opponent from getting close or escaping a submission attempt on the ground. All of these factors are disadvantages in a fight with a Brazilian jiu jitsu expert, because his strategy will be to close in, take the boxer down and apply a submission hold. The typical boxer would have no experience or training to prevent this. The one opportunity for the boxer to win will be with a powerful knockout strike.
No Top-Level Fights
Despite Gracie's victory over Portugal and many similar victories for Brazilian jiu jitsu since, boxing fans can still point to the fact that no world-class boxer has ever participated in these matches. Gracie was one of the best jiu jitsu fighters in the world in 1932, but Portugal was not one of the world's best boxers. The question of who would have won in a fight between Gracie and the world heavyweight champion is still an open one, because Louis refused the fight. To a champion who fights for a living, there is little incentive to participate in a mere challenge match for what would amount to bragging rights or at best a greatly reduced sum of money.
Boxing Vs. MMA
The debate about the relative merits of boxing and Brazilian jiu jitsu has largely shifted to one about the merits of boxing and mixed martial arts. MMA fighters typically train in both boxing and Brazilian jiu jitsu, as well as muay thai kickboxing. This means an MMA fighter will usually have skills at kicking range, striking range and grappling range, but would not have as much expertise in any one of those ranges as a specialist would. The question is whether a world-class boxer could use his expertise in the striking range to defeat an MMA fighter with fewer striking but more kicking and grappling skills. Unless champion boxers begin to compete regularly in MMA events, the question will remain.