I love dogs, but if the wild animals have already engaged the dog, I'm taking advantage of the distraction and gettin' out of Dodge, weapon of choice being a good pair of trial runners!
If a cougar isn't on my back, it's rock and stick time. Predators don't like getting hurt and making yourself look difficult helps. If the cougar has jumped me, yeah, I'd like a good stout knife.
With wild dogs, I'd go for a stick. Like the cougar, they can't afford to get hurt.
Grizzly bear? Time to back off. When I was a kid, saw grizzlies in Yellowstone take the top off a steel Coleman cooler like it was cardboard. The power they have is just amazing. I'm afraid a pissed-off grizzly mom bear would take a stick out of your hand with one swipe and maybe you hand with it! I don't know if I could ball up and play dead while getting mauled, so I'll take the big knife option if actually being attacked. Like I said, if the bear is busy with the dog, I'm clearing out.
Like the old saying goes, if you are being chased by a bear, you don't need to be the fastest in the group, just a little faster than the slowest guy.