Yes, dead is dead but the way of dying is much different. I would rather provide a quick death for an animal than have it die a slow one from starvation, dehydration, animal attack and/or injury.
Now i know that this may be seem, well, blunt, but why not kill them? I mean, why not kill 'em and have rabbit stew? We have snowshoe hares here but I'd imagine they'd be tasty....just an idea..