Mihawk never set out to become the World's Strongest Swordsman, he only set out to fight enjoyable battles against powerful people. That's where he is so different from Zoro, Zoro wants to be the strongest and wants to win. That's not Mihawk's goal at all. That's why Mihawk will enjoy losing to Zoro at some point, as long as he gets a good fight out of it.
That's why Mihawk doesn't one shot Zoro in the East Blue, that's why Mihawk gets "stalled" by Vista, Croc, Zoro in the East Blue. Because he takes fights slowly to try to enjoy them.
Just look at this test of "difference" between him and Whitebeard, he sends a unamed slash without haki, he wanted tto start a conflict to enjoy a fight against Whitebeard, but he couldn't get that in the middle of the war.
That's why the way Mihawk fights is so interesting to me. Other characters in the series fight to win, survive or achieve their goal. Mihawk's goal is enjoying the fights with opponents he sees value.
2nd - Mihawk, even with his little screen time, has an actual character arc and development. It's very subtle. He starts as a complete lone wolf, until he sees how Zoro and Luffy are with each other and their goals, lifting each other up in the East Blue.
Then Mihawk sees Luffy again during Marineford, getting the help from a bunch of people, even from previous enemies.
And finally, Mihawk sees Zoro, a man who held power and winning above everything, kneeling before him to ask for training in the name of helping Luffy, not achieving his own dream.
That slowly made Mihawk more open to having allies and friends, that's why he decided to teach Zoro and let Perona stay on his island. He is slowly being more open to the idea of being part of a crew and counting on other people.