Kakashi needed sharingan and Ninja hounds to find Zabuza in his Hidden mist jutsu. Since Asuma doesn't have those, I don't think he could win. Zabuza wins.
Zabuza wins. Asuma has no way of fighting in the mist not even sharingan can see through nor does he have any other ways to sense Zabuza since he has silent killing techniques. Even Kakashi had to rely on smell from his ninja hounds which Asuma cannot do.