Protection > Personal > Axe Axe
The only time I could see an axe coming in handy as a weapon would be if you are hiking...
While it might seem a little exotic to think of using an axe for self defense, if you might want to consider it if you are out using your bushcraft skills.
There are a lot of axe throwing locations, so you might as well take advantage of them. In real life though, you probably don't want to throw a weapon at a person. If you miss, you just gave them a weapon.