I may seem like the odd man out here, but personally, I'd go for the bow.
With enough practice, you can become sufficient enough to hit anything. They come in many different configurations, and can be tuned to make it as "personal" as you would like. They can be lightweight and portable. And they can be used to kill anything. There are hundreds of different arrow configurations as well.
While packing a bow, for survival, or any situation, you can make it extremely versatile. You can carry some small game tips, as well as field tips and broadheads.
Yes, on some game, you risk shooting them and then having to track a wounded animal with an arrow stuck in it. But for a survival situation, I feel it would be ideal.
Someone mentioned earlier about shooting groundhogs with a pellet gun. Maybe we just have really tough groundhogs here, but I'd would try shooting one again. I shot one with a pellet gun (I don't remember the make, but it was a .177 caliber), and the damn thing chased me all over the place. It was like flicking a bear in the ass with a rubber band; it didn't do a thing.
As fun as pellet guns may be, I'd still take a bow over one any day.
Kris