[quote=@Blizz]
[@Ogobrogo]

Earth style chakra is rigid and stiff. It’s not a good idea to swing a sword at a rock.
[/quote]

I mean, Asuma threw his Wind-infused Chakra Blade through a tree and pierced into a sizeable rock. The tool was just fine afterwards.

Considering that Wind and Earth elements in the series don't directly interact with one another, ninja tools - including swords - have displayed incredible feats of durability, and Mizo and Kimiko are both only Genin/Chunin level kunoichi, I don't really think either of them have an inherent advantage over the other. 

Maybe if it was Kimiko's wind-infused sword on a normal rock or a normal sword on Mizo's Earth-infused bracers then it would be a bit more one-sided. But the two clashing? I dunno. Maybe I'm missing something here?