The sharpness of a sword depends on various factors, such as the quality of the blade, the skill of the swordsmith, and the purpose for which the sword was designed. Both katanas and European swords have been crafted to achieve exceptional sharpness.

Katanas, specifically traditional Japanese katanas, are renowned for their sharpness and cutting ability. They are designed with a single-edged blade and a curved profile, allowing for efficient slicing and cutting. The traditional sword-making techniques used in crafting katanas, such as differential hardening and meticulous edge honing, contribute to their reputation for sharpness.

European swords, on the other hand, encompass a wide range of sword types and designs. Many European swords, particularly those used during the medieval period, were also known for their sharpness. European longswords, for instance, were versatile weapons with a double-edged blade and could be honed to a very sharp edge.

It's important to note that the sharpness of a sword depends not only on its design but also on the craftsmanship and maintenance of the blade. Skilled swordsmiths in both Japan and Europe have demonstrated the ability to create swords of exceptional sharpness.

Ultimately, determining which type of sword is sharper, be it a katana or a European sword, is subjective and can vary depending on the specific sword, the quality of craftsmanship, and the intended use of the weapon.