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I think it has a fair enough chance to compete. Considering that it's specifically stated that Jyuuken can destroy chakra entities, and Susanoo is an entity of chakra.... there's no reason it cannot in terms of principle. Given a skilled and developed enough Jyuuken user, a Susanoo could be destroyed. Though more likely it would be more like Jyuuken destroys that specifically targeted area as opposed to just one Poke suddenly blowing up the entire thing.... then again, Neji did blow up a spider using Jyuuken

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But will Jyuuken ever be shown breaking a Susanoo?! Not a chance. Why!? Character development.
Primary Antagonist: Madara Uchiha, Susanoo User
Primary Character: Sasuke Uchiha, Susanoo User
Side Character: Hiashi Hyuga, Jyuuken User
The only person who's shown the full extent of Jyuuken is Hiashi Hyuga, and he's a side character with less panel time than Iruka (I think). Kishimoto has been rather awful at developing the Side Characters. No other Hyuga has had any development to display this power to its fullest extent. Put simply, Kishimoto has hardly shown the fundamental workings of Jyuuken enough for anyone on Narutobase to even consider it (well... the general population of it anyways).
In theory, yes it can. However, no Jyuuken user has been shown with the scale and skill to do so other than Hiashi Hyuga. No Hyuga has shown the scale to efficiently deal with a Perfect Susanoo.