Despite the close association between Zen and swordsmanship in the popular mind, the Mikkyo sect of Buddhism was actually much more closely connected with the classical Japanese martial arts. Most of the Japanese sword traditions include instruction in Mikkyo at their higher levels, or once did before that information was lost.
So what is Mikkyo? Mikkyo is “esoteric” Buddhism, a version of Vajrayana practice. It involves a lot of traditions that would generally be seen as occult or magical by most modern people. Mikkyo practitioners use everything from special hand symbols to elaborate visualizations to magic spells to achieve their goals. Those goals are ultimately part of the quest for enlightenment, as in every other form of Buddhism. However, they can also be used for more mundane purposes.
For instance, if you know you have to go into battle the next day, you can perform a Mikkyo visualization to invoke the power of a warrior deity, cleansing yourself of fear before facing combat. Mikkyo practices are frequently a type of self-hypnosis or cognitive therapy, in which the practitioner uses the ritual to alter his own thought patterns in some beneficial way.
This accounts for the popularity of Mikkyo among the samurai. Because Mikkyo practices were literally believed to have occult powers, they could be used as a highly effective method of psychological self-discipline, increasing the chances of surviving combat.
Zen, which eschews any kind of supernatural talk and emphasizes the need for decades of meditative discipline, just couldn't offer such quick and practical results.