In a sense, Zoro has ready surpassed Mihawk. Back in Skypiea, he said he didn't like to fight with a motivation, but felt one coming on when Chopper was hurt. Zoro has developed motivations outside his goal, come to care about the crew, and their dreams, and fight to protect.
Mihawk is still being shown to be singular minded, aside from his title he has nothing. No friends (Perona went back to Moria), no drive, nothing to protect or go after.
Zoro found outside motivation, Mihawk has none.