Link would win.

did you ever observe how fighter actually attacks? he NEVER actually makes physical contact with his enemy, meaning he must have some sort of psychich fighter powers, like sword lazers, which are like lazers but sword powered !1!!!111!!!
The Fighter doesn't have a magical sword, Square was just to lazy to make him (and everyone in FF 1-6) move more than 2 feet.

As for the actual battle, here's how it'd go:
Link starts by filling the Fighter with Silver arrows and stunning him with the Boomerang. When Fighters almost there Link starts running around, with Fighter following at about the same speed, maybe a little slower since he's full of holes. Link drops bombs will he runs, effectivly killing (or fatal wounding Fighter). The End.