The comparison between a tachi and a katana in terms of which one is "better" depends on the context and the specific criteria being considered. Both swords have their own unique characteristics and intended uses. Here are some factors to consider:

1. Blade Design: The tachi and the katana have similar blade shapes with a curved edge, but there are some differences. The tachi typically has a more pronounced curve compared to the katana, which can affect the cutting and slashing techniques. The design of the katana, with a gentle curve, is known for its versatility in both cutting and thrusting.
2. Historical Usage: The tachi was historically used by samurai warriors during earlier periods in Japan, primarily from the 10th to the 16th century. It was often worn by samurai on horseback and was designed for mounted combat. The katana, which evolved from the tachi, became more prevalent during the Muromachi and Edo periods (14th to 19th century) and was used by samurai both on foot and on horseback.
3. Purpose and Function: The tachi was primarily designed for use on horseback, emphasizing reach, power, and cutting ability. It had a longer blade and was suitable for striking opponents from a mounted position. The katana, while also used on horseback, was more versatile and became the primary weapon of the samurai. Its design allowed for effective cutting, slashing, and thrusting techniques in various combat scenarios, both on foot and on horseback.
4. Wearing Style: The tachi was worn with the cutting edge facing down when sheathed, enabling quick drawing and immediate use while on horseback. In contrast, the katana was worn with the cutting edge facing up when sheathed. This difference in wearing style reflects the different combat situations and needs of samurai on foot or on horseback.

Ultimately, determining which sword is "better" depends on the specific requirements, the skill of the wielder, and the intended use. Both the tachi and the katana have their own advantages and purposes. It is important to consider the historical context, intended usage, and individual preferences when comparing these swords.