A friend did point out to me that some of the Doc Savage stories got pretty fan-wankish, with him ripping though metal with his bare hands or some such. That might give him the edge in strength.
I go with Conan for the reasons smiling bandit stated. If I needed someone to save the world I’d go with Doc Savage, but a one on one fight? Conan all the way. Doc Savage is a renaissance man, Conan is a professional killing machine.
If it was Doc Savage vs. Tarzan, the outcome has been recorded for posterity.
You know, I have a copy of Farmer’s Doc Savage: His Apocalyptic Life somewhere. It was OK, if a little spotty. There’s no excuse for A Feast Unknown, though.
RR
But I do. I have all the original Lancer Conan books, the ones edited by Lin Carter and L Sprague de Camp. I count these, and Lester Dent’s original Doc stories, but not the one by Farmer.
We must define what age each will be before this can be a meaningful 
discussion.
Young Conan left home at 15 and was big, strong, and green. By the time he was 17 he had a great deal of practical experience with street fighting, wizards, thievery, women, etc.
Doc at 15 was still in training, I believe, or had just joined the army. Then Doc spent time in the prison camp where he met the rest of the team. They escape when he is 17, so his experience at that point is rather limited.
I suspect that if they meet when both 17, Conan wins easily.
Later in their respective lives, a lot more happens.
Farmer did a slightly cleaner take on this, which was published as both sides of an Ace Double - Lord of the Trees (mostly about Tarzan) and The Mad Goblin, mostly about Doc. They are two parts of the same story.
Which contains the epic hand-to-hand battle (on a log over a canyon, IIRC) between Tarzan & Doc. I won’t spoil the ending.
So maybe we need a round-robin cage-match setup: Doc vs. Tarzan, Tarzan vs. Conan, Conan vs. Doc. Who else should be included?
Muscles will bulge! Shirts will rip! Thews will strain! Sinews will <something>!
Shirts will rip? I think the identity of the next combatant is absolutely clear.
Quite clear; and the victor a fait accompli.
Thundar vs. He-Man.
What?
Oh, and I vote for Conan. I think his sheer brutality would give him the edge.
More like King Log vs. Dr. Mengele.
At least Conan believed in free will.
I ate lunch with my mother today and asked her the OP’s question. She thought for a second and said “Conan. He’d fight dirtier.” 
High five yer mom! 
And the comics? ALL his appearances?
What kind of terrain are we dealing with?
City? Doc could exploit it quite well.
Wilderness? Conan takes it.
Arctic? Both sides are very arctic-proficient.
A bull hide staked to the ground. Anyone whose feet leave the hide gets skewered with a crossbow or shot with mercy bullets. No fair taking weapons away from judges or using judges as blunt instruments.
Then Doc wins.
He knows Judo. Very, very well!
Conan goes flying, gets zapped for leaving the mat.
End of fight.