I don't think it really matters. Both rounds will shoot all the way through a CAT, even a big cat. Animals are rarely impressed by a relative handful of ft/lbs, what your gun has written on it, or how many rounds it holds.
What they do notice is being HIT, and where they get hit. Choice of caliber (and ammo load) doesn't matter as much as your ability to hit the right spot with the gun you are using.
I agree that the cougar is usually a close-range ambush predator, but not always.
This made me chuckle. Tried to think of a "long range predator" (other than man) ...couldn't.
Or at least not one dangerous to man. The Archerfish might qualify, if I were an insect...but everything I can think of has to actually touch you to harm you, oh wait, just thought of one, the Spitting Cobra,.
Point here is, that while a predator stalking you IS a threat, one you need to be aware of, you're not at physical risk until they get close enough to touch you. Shooting one across the meadow because it was headed your way may not be a justifiable act, compared to shooting when they are a double handful of yards away and charging , or close enough to pounce on you.
Very small pistols, while easiest to carry are notoriously difficult to shoot accurately, even at close range, which I think matters more than your choice of caliber or capacity. Both rounds are capable of doing the job, but only if the shooter can hit a vital spot.