Probably a duel until one is unable to continue or yields. They may have honor, and they'll fight to defend it, but they themselves don't hold an overabundance of pride. Honor is how others see you; pride is how you see themselves. They fight for honor, but they won't kill for their pride. (Took that from the Age of Fire series, a book series told from the viewpoints of dragons in a world where they are coming back)