Realistically a snare is a great tool for food as well as dead falls. Slingshot isn't a bad deal. I have taken a few rabbits with a throwing stick with decent luck.

Snare wire is great because it can be used for the intended purpose, lashing, or a string on a bow.

Of your two choices a slingshot would be mine choice.

I think I would like to try and make an atlatl sometime. Its an interesting tool