Whereas axes mechanically bridge the gap between maces and swords, the Hunting Sword is what lies between axes and one-handed swords. They have decent values of slash damage, low to moderate stab damage, and an above average amount of blunt damage that is higher than any other type of one-handed sword, or longswords (save the Thumper).
Just like axes, this type of weapon excels against enemies that have low amounts of armour.
The advantage here is being able to have "some" damage qualities of Axes, with both speed and combos that are unlocked in the sword skill tree.