An (large adult male) human (maybe with a knife or stick) at least has solid odds against a cougar/puma/jaguar/leopard, particularly if not taken unaware; a grizzly bear is going to win, and your only real chance of survival would be if it breaks off the attack. Even with a firearm, a brown bear is terrifying.
The brown bear is more formidable like you said. But your odds are terrible against a full-size cougar or leopard one-on-one; even with a knife or stick. Even if you're facing the first rush (unlikely), they'll have better reach and strength to parry your first swing. Then they'll get to your neck and it'll be over. Or they'll slash out your legs or abdomen and you'll bleed out.
A full-size large cat has killed for just about every calorie it has ever consumed. All those encounters with animals fighting for their lives and it's still here.
I think it was in Jim Corbett's book, The Temple Tiger and More Man-eaters of Kumaon (Or it may have been one of his earlier books) where he describes being pounced on by a big cat while in his tent one night - From memory a Tiger - and the only thing he had at arms reach to defend himself was a small cheese knife on his supper plate. He managed to get lucky and kill it with the little knife.
Several years later, he got into an argument with a shop assistant while trying to describe how he had killed a Tiger in India/Africa (memory escaped me) with a similar little knife as he found in the shop. After the shop assistant didn't believe him, Corbett got angry, abused him and was then arrested for causing a 'public hysteria'... Or so the story goes.
A Bit of an off-topic point, I know.. But I thought it was interesting to bring up. I definitely recommend reading Jim Corbett's work, it's an interesting view of life when there was a real chance of you being eaten by a man-eater, and seeing how his work hunting man-eaters led to the establishment of the Corbett national park in India.
Thanks for bringing that to attention. Hadn't heard of Corbett before. I'm not immediately sympathetic to a guy killed a bunch of big cats. If they were man-killers, ok, maybe that's reasonable. But I'm still suspicious about who would take up that job.
The claim of killing a tiger with a cheese knife...yeah right. Tigers hunt big prey with sharp tusks and horns. They fight other Tigers from time to time. A dude taking one out with a cheese knife isn't even plausible.
No problem. Remembering that this was a different time, and in most cases the animals only became problem man-eaters after something like an injury has forced them to target people. Corbett's books are a fascinating read because even though he's a hunter, he's very interested in conservation of the habitats.
The cheese knife thing is a bit of a laugh, but again - having read enough about the man, I wouldn't have put it past him.