In my opinion, Jin would win. And for the very reason that Haku and Foxy said that Mugen would win.
It's been a long time since I watched the anime, but if I recall correctly (and evidently I do) Mugen uses an incredible, flashy style, deliberately making excessive and inefficient movements with the intent to disorient and distract.
Yes... against an ordinary opponent, this seeming randomness would be an advantage. But against Jin, who has seen Mugen fight before, has fought by his side and I think even fought against him at some point, it's a disadvantage. Mugen's movement are not new or unfamiliar to Jin, he is used to Mugen's fighting style by now. And so instead of being distracted or disoriented, he would simply strike with efficiency where Mugen is not. Mugen would lose... assuming that they are both equally skilled at their own styles of fighting, and that they are both familiar with each other's style, Jin would win because his style is more efficient.
You could argue that Mugen would just be less flashy, then. But then Mugen would be fighting in a way that he is not used to, and he would be making a conscious effort to do so... this will still give Jin an advantage, because Jin would be fighting naturally.