If I can kill someone shooting at me with a gun with my fists or a freaking baseball bat I'm sure I could take him out with a crossbow.
Not to mention shooting at things with a Bow or Crossbow is about hitting weak spots, the neck, joints, the heart.
it takes a more tactical play style for a bowman
Bows and crossbows are obsolete
yet they are still used today, for survival in the more remote places in the world, and By Modern Hunters.
the bow is a weapon over 5000 years old. and would fit well In a tribal setting.
but if you need some reasons (be them modern reasons) from a survivalist point of view check this http://willowhavenoutdoor.com/featured-wilderness-survival-blog-entries/the-take-down-survival-bow-arrow-6-reasons-you-should-consider-owning-one/