Two totaly different types of killing. Arrows are ment to cut through vital organs to induce bleeding. Indians knew that you cut the lung they deflate and bleed. Flint and Obsidian heads are very good at this. In fact Obsidian is sharper than any steel blade.

Bullets kill in the transfer of energy. The bullet flattens to transfer the energy into the animal, creating massive shock. If the bullet passes through the vitals it can be similar to an arrow but does not cut like an arrow is intended to.

So sure a 9MM through the vitals will kill. Its range isn't going to be great but at close range sure.
However, 9MM isn't a very good man stopper. So on something tougher like a deer I wouldn't use it unless I had to. (Like to survive)