Honor and justice go hand in hand. If there is no honor where would we find justice? If one has great respect, loyalty, integrity, and duty to and for humanity and life then he or she is exhibiting honor. This in turn leads to being able to render justice. One without the other is useless.
In my opinion, honor is not more important than justice. Honor is the emotional part of the ego that is wounded when the Ego isn't granted it's wants and desires. Justice on the other hand is the practice of recompense for a wrong or loss that can be personal or personal property, or material goods.