There isn't much difference between sword and axe, both are blades with a hilt. If Zoro wins against a Harald wielding a sword, he will beat a Harald who wields an axe. If Zoro cannot beat an axe-wielding Harald, he will be an inferior swordsman too.
People keep talking about everyone using a sword just as a weapon of choice, but using swords is also just a weapon of choice for Zoro because he grew up in a swordsman Dojo. Swords being the weapon of choice for Roger, Xebec & co. means, that Roger, Xebec & co. are at least as powerful with a sword as with any other weapon (axe, naginata, etc.), if not stronger (most likely) because weapon of choice means they are most perfectly accustomed to that type of weapon.