Think about it this way.
Mihawk is Goku, Zoro is Vegeta.
Mihawk doesn't necessarily want the WSS position. It was just something that came to him through testing his strength against others and constantly pushing himself to the limits. He is constantly bored with life because no other swordsman is left to challenge his skill.
Zoro is different. He seeks the WSS position. Not only that, but he vowed to never lose against any other swordsman, no matter the cost. Once he reaches the top, he will be satisfied with no other rivals to challenge him in that position.
This is what makes Zoro a conqueror, in my opinion.