“Always” is a very definitive statement. But let me tell you that there is a lot more energy transferred into the tissues around the bullet trajectory. Watch YouTube videos of bullets going through ballistic gel to see what I mean. They don’t just punch holes in people they also have a huge cone of severely damaged tissue surrounding the hole. Also they can break into fragments going different directions and if they hit a bone can even bounce around doing more damage. You just aren’t likely to have that as much with an arrow because there is less energy and the shaft will stop it from richocheting in a different trajectory.

Also the arrow may help slow blood loss while still in place whereas a bullet is not going to do that.

About the only thing that a bullet has going for it over an arrow is that depending on where it is you might be able to stop the bleeding (via surgery for example) but don’t necessarily need to dig all of the bullet fragments out. I’ve seen quite a few patients who have bullet fragments retained in their body. No way you can leave part of an arrow though.