The Katana is the last weapon unlocked by the Assassin. It is the most powerful Melee Weapon you can get, dealing 150 damage, with a critical bonus of 30%. The problem is not even its' slow rate of fire--unlike the Nine Iron and Bat. If you miss, you will get a quick chance to recover, and that's more than enough. If your Assassin is level 50, you should have a 50% critical already, add that on to the Katana's 30% chance gives you a 80% chance of a critical hit. Therefore, it will almost always kill with just one slash. It can kill any kind of Assassin, even up to level 50, without a critical in one slash.
It's comparable to another late unlock, the Machete. The Katana gains the upper hand in damage, whereas the Machete has fire rate to its advantage. It depends on the circumstances you often find yourself in. If you prefer 1v1 fights, then the Katana is for you. If you are facing multiple opponents very often, then the Machete's faster fire rate is a lifesaver. Either one is a good choice, it comes down to personal preference. Even though, the Katana should have the upper hand in a Katana vs Machete fight.
Increased critical chance
Increased critical damage
"Extremely sharp. Hold onto your limbs!"