Tidus, because if he started losing, all he'd need to do is get his dad to pwn Shuyin.

Seriously though, I believe Tidus would win because of his clarity of thought. Shuyin, after spending 1000 years in the Den mourning the loss of Lenne would make him more than a little mad, causing him to settle on one strategy and open himself to weaknesses (such as love), whereas Tidus would think (towards the end of the game at least) his actions through and hopefully come to a reasoned strategy that would be flexible, thus giving Tidus greater battle skill over Shuyin. However the fact that Shuyin can possess others would raise Shuyins chances of winning, eg possess Tidus and get him to run himself through with his Caldebolg... Also, iirc, wasn't Shuyin a Zanarkand Warrior before he died?

My thoughts at least...