The Landskencht in Etrian Odyssey Untold: The Millennium Girl is able to specialize in either in either Swords or Axes. I'm able to get some idea of the differences between the set-ups based on the classes skill tree, but I'm curious how Axes and Swords themselves differ, independent of the skills. A quick look at the Shileka's Goods suggests that Axes have more damage than Swords, but do different types of damage. I'm not sure how different damage types differ, and my limited dataset would suggest that axes are superior to swords because of the additional damage. I'm assuming this isn't the case, and that there's more differences between the two to make them more balanced.
How do axes and swords differ?