I wouldn't necessarily say that bow hunting is better than gun hunting, they're just different. Since you are stating that bow is better than gun, make your paper argumentative and possibly use statistics.

One thing archery does require, for the most part, is close quarters with your quarry. For me, it's a bigger "rush" to have a deer 20 yards away vs. 200 yards away.

As far as gun hunting, just between you, me and the lamp post, I couldn't hit the broadside of a barn with a rifle.