I prefer the sword because of the fast recharge and its ability to combo easier. While shields counter it, keep in mind that using the shield renders its user unable to attack and reduces his mobility significantly unless he's using kill aura and noslow. Additionally, pre-1.11 shields block 2/3 of the damage instead of all of it, so the user will still take some sword damage. Because of this property, most people will not use a shield in pre-1.11 combat (more likely used in post-1.11 to block all the hits). You can mitigate or eliminate that weakness entirely by bringing an axe just to land the first hit or to disable the shield -- in other games, lava or fire will also do the trick.
More pros/cons of the two (from an old post). This also assumes we take armor penetration into account, but this server has that mechanic disabled.
https://www.cubecraft.net/threads/sword-or-axe.134038/page-4
Sword:
+Scales well with sharpness since sharpness increases the DPS by 1.6 on the first enchant. Subsequent enchants increase the DPS by 0.8.
+Can be enchanted with fire aspect, effectively bypassing shields.
+Some crowd control, though this bonus is negligible unless it's 1.11.1+ combat with the sweeping edge enchant.
-Penetrates less armor than the axe (doesn't apply to Cube since armor penetration is disabled).
-Weaker than fire swords and axes for first strikes and chasing.
-Low damage for wood and gold swords. Even a gold axe has higher DPS than a gold sword!
Axe:
+High burst damage means it's good for chasing or first strikes.
+Paired with crits, it can tear through more armor.
+Benefits more from strength potions thanks to its high burst damage. This means it will pierce through even more armor than a sword with strength.
-No fire aspect and knockback enchants. Exception: custom-created axes in SG have knockback.
Any weapon works in the hands of a kill aura user because of crits and 100% accuracy. Just kidding; don't ever do this.
