i think i'd personally feel safer with a 10mm. I don't know for sure, but i would SPECULATE that wild animals in the woods have much tougher skin, muscle tissue and bones than humans....so you'll want something that'll easily pentrate through all of that and hit vital organs in order to stop the damn thing from even touching you. But that's just me.
Good luck on your search. I hope you'll never actually have to use it for that situation. I know i wouldn't!