Are we talking about in a fight or just who is the better character? If it's the latter than Tidus wins. If it's a fight then I'd say Lightning destroys him. Unfortunately, Tidus seems to be one of the weaker solo fighters when it comes to the protagonists. He'd probably be the first one down in a fist fight too. He's quite confident in gameplay but he lacks any feats, which are what really count.
So over all Tidus>>Lightning as a character but Lightning>>>>>>>>>>>Tidus in a fight. It would be fun to watch though.