Depends on what you're fighting against/using it for.
Katana in terms of speed, weight, cutting potential and beauty. Broadsword in terms of power, versatility, durability and when fighting against an armored opponent.
I prefer the Katana, if we're talking in terms of aesthetics and not convenience, mostly because of the mystique and culture around the weapon, and how it's portrayed ridiculously inaccurately in modern media, such as in anime, manga, comic books and movies.
