This is a good question. Rainsford wins at the end, even though general Zaroff had the advantage (dogs, Ivan, and knowledge of the island). This shows that Rainsford is the superior hunter. Rainsford has three things going for him.
First, Rainsford is an experienced hunter, probably more experienced that Zaroff. This comes out, because Zaroff says that he read all of Rainsford's books on hunting. This means that is some sense Rainsford is Zaroff's teacher.
You see, I read all books on hunting published in English, French, and Russian. I have but one passion in my life, Mr. Rains. ford, and it is the hunt."
Second, Rainsford has travelled around the world and learned various ways to hunt. For example, Rainsford used a Burmese trap to take out one of Zaroff's dogs.
"You've done well, Rainsford," the voice of the general called. "Your Burmese tiger pit has claimed one of my best dogs. Again you score. I think, Mr. Rainsford, Ill see what you can do against my whole pack. I'm going home for a rest now. Thank you for a most amusing evening."
Finally and arguably most importantly, Rainsford was armed with survival and desperation. So, the hunt may have been a game for Zaroff, but it was not so for Rainsford.