Well, to defeat Sasori, Konan needs to crush Hiruko, a feat that Chiyo stated she couldn't accomplish
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, even when she had her Jikki Chikamatsu that soloed a castle. Only with Sakura's superhuman strength were they able to destroy the puppet. And then there are the puppet traps inside Hiruko that one hit from them can be a game finisher.
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In addition to his skill in using Hiruko's tail for both defence (
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) and offence
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, Sasori can arguably defeat Konan with Hiruko only; especially since Konan has pretty much no way of crushing it for reasons I mentioned earlier. But even if she somehow was able to get around destroying it, 3rd Kazekage puppet finishes her off.
Konan is strong, but Sasori has too much for her. With that being said, I believe Konan would push Sasori to mid difficulty.