bell curve

The axe deals more damage for a single target so it is better for a 1v1 encounter, but if you are fighting multiple targets, the sword is better because of the sweeping attacks that can hit up to 5 targets at the same time, depending on how close are they to the sword / you / each other

I personally prefer the axe because it has multiple uses, but sword is also goated

Mace users:

they have they're ups and downs but neither are as good as the trident in bedrock

It depends on the version, on Java it’s the axe, and on bedrock it’s the sword.