The Long Swordsman is simply a better version of the Broad Swordsman. It has more hit points, attack, and armor, though by the time they can be trained there are better infantry unit choices at the Academy. They are good for massed attacks due to their cheap cost. The Long Swordsman can be upgraded to the Legion once Fanaticism is researched.
“The long sword represents the culmination of infantry weapon development in antiquity. It was designed for both piercing and slashing, combining the best of both the short and broad swords. The long sword was made possible first by advances in bronzeworking and improved by the discovery of iron. Some historians believe that the development of long swords by barbarian cultures was a key factor in the catastrophe of 1200 BC, when most of the civilized cultures of the Mediterranean and Middle East were overrun. The long sword in various forms remained an important military weapon until the advent of gunpowder.”