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The numbers say

Battle Axe hits harder per shot — 55 vs 45 (a 10 point gap).

On theoretical sustained DPS (damage ÷ time between shots, ignoring falloff and reload), Battle Axe comes out ahead at ~79/s vs ~64/s for Katana.

Katana is the cheaper unlock (45 Keys vs 50 Keys).

Battle Axe — damage55
Katana — damage45
Battle Axe — fire rate1.4/s
Katana — fire rate1.4/s
StatBattle AxeKatana
Categorymeleemelee
Cost50 Keys45 Keys
Damage5545
Fire Rate0.70s0.70s
Ammo
Reload

Battle Axe

The Battle Axe is a weapon which is designed to dominate melee encounters. While its sheer power comes at the cost of reduced movement speed, skilled players can leverage its strengths to great effect in both offensive and defensive scenarios.

Katana

The Katana is a well balanced melee used by players of all skill levels, it has a solid M1 damage[citation needed, who said that?] and has a unique ability to deflect bullets back at opponents, making it a common choice for countering high-DPS weapons.

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