The OP does specify “one-on-one,” which should rule out divine aid.
But was it a grizzer bar, pilgrim?
I’ll take Herakles. Taking the weight of the sky is one hell of a thing, especially considering that the only other being who could pull it off was the strongest of the titans. Further, single-handedly diverting rivers is a class up from anything Samson managed. Also, when Samson was betrayed by a woman, he lost his strength and was taken into captivity for years. When a woman turned on Herakles, he was taken up into Olympus. I don’t know that Herakles ever killed 1,000 men at a go, but I don’t think you could have FOUND 1,000 men in Silver-Age Greece who would have waded in against that guy. Herakles by a hair, its root, and a scalp.
I believe Jack o’ Diamond was the [del]grizzer[/del] grizz-i-ly b’ar. 
Atlas wasn’t given the job because he was uniquely qualified, he had it because he sided with the titans and Zeus figured that being punished with the 24/7 task would keep Atlas out of trouble. Also, Atlas’s brother was sent to the underworld so having Atlas in charge of holding up the heavens prevented them from meeting and conspiring a second time against the gods.
Also, when Samson died, he was all “You jerks are going with me” and killed 3,000 men in his final efforts. Hercules just whined a lot and was all “Waah, my shirt hurts, someone set me on fire” until the gods were like “Sheesh, just take him up to heaven already so he stops crying”.
So Samson was way more bad ass in death than Hercules was.
Yeah, but Samson didn’t have to put up with that f****** centaur and that freak with the panpipes. And you just know Helena never put out.
No-Weapons smackdown? Has to be Samson. He’s famous for his improvised and unarmed combat skills - killing 1000 Philistines with the jawbone of an ass, a lion with his bare hands, pulling down the Temple on all those Philistines with his bare hands, etc.
Herakles is more known for his skill with various weapons. Most of his feats involve him having weapons to hand. Sure, he’s super strong, but a no-weapons smackdown plays to Samson’s known talents.
Divine aid is such an intrinsic part of both characters that it amounts to a virtual superpower. Further, if the divines want to be involved, you won’t be able to stop them. They’re divine. You…aren’t.