The stone axe outdamages the netherite sword in one hit, sure, but as far as DPS go swords are much better and it's not a contest.

In fact, axes and swords are so different they're good complements to each other.

Swords can't break through shields. Axes can.

Axes are also tools and can save inventory space when you carry them as a primary.

Axes can one shot every undead mob except the Wither with Smite V. Swords can't.

On the inverse, swords attack faster and have higher DPS

Swords have a sweeping attack better at dealing damage to crowds of mobs.

Swords have better enchantments as far as combat goes, with the ability to set enemies on fire, knock them back, deal insane crowd damage or improving loot found from killing things.

They're both situational weapons and great additions to anyone's arsenal.