Caps, hands down. Besides the fact that Conan doesn’t have anything that could penetrate or even dent Captain America’s shield, take a look at what Conan is up agianst:

“Captain America has no superhuman powers, although as a result of the Super-Soldier Serum and “Vita-Ray” treatment, he is transformed from a frail young man into a “perfect” specimen of human development and conditioning. Captain America’s strength, endurance, agility, speed, reflexes, durability and healing are at the highest limits of natural human potential. It has been established that Rogers’ body regularly replenishes the super-soldier serum; it does not wear off.

The formula enhances all of his metabolic functions and prevents the build-up of fatigue poisons in his muscles, giving him endurance far in excess of an ordinary human being. This accounts for many of his extraordinary feats, including bench pressing 1100 pounds (500 kg) and running a mile (1.6 km) in little more than a minute. Furthermore, his enhancements are the reason why he was able to survive being frozen in suspended animation for decades. Rogers is also unable to become intoxicated by alcohol and is immune to many diseases.[citation needed]
Mentally, Rogers’ battle experience and training make him an expert tactician and an excellent field commander, with his teammates frequently deferring to his orders in battle. Rogers’ reflexes and senses are also extraordinarily keen. He has blended Judo, Western boxing and gymnastics into his own unique fighting style and is a master of multiple martial arts. Years of practice with his indestructible shield make him able to aim and throw it with almost unerring accuracy. His skill with his shield is such that he can attack multiple targets in succession with a single throw or even cause a boomerang-like return from a throw to attack an enemy from behind. In canon, he is regarded by other skilled fighters as one of the best hand-to-hand combatants in the Marvel Universe.
Rogers has vast U.S. military knowledge and is often shown to be familiar with ongoing, highly-classified Defense Department operations. He is an expert in combat strategy, survival, acrobatics, military strategy, piloting, and demolitions. Despite his high profile as one of the world’s most popular and recognizable superheroes, Rogers also has a broad understanding of the espionage community, largely through his ongoing relationship with S.H.I.E.L.D. He occasionally makes forays into mundane career fields, including commercial arts, comic book artistry, education (high school history) and law enforcement.”

The way I see it, Conan charges into battle, Caps throws the shield, which bounces off his head before returning to him. Conan in a daze, Captain America does a few back flips and kicks him in the head so hard his brains ooze out his ears.

In JLA/Avengers (I count that as cannon due to the reappearance of the cosmic egg) Cap was shown as being on equal terms with Batman in terms of skill. Thats alot of fighting skill.

Conan versus Captain America…

So, Warrior born versus Warrior-created?

Or, Barbarian king versus someone who thinks a shield is a really good idea for a weapon?

Or, possibly, Awesomely skilled fighter who kills without a second thought versus awesomely skilled fighter who will try everything in his power to incapacitate.

Conan wins this. They are both in the absolute peak of physical condition, and Rogers nigh infinite stamina, on paper, sounds like it’ll win it for him. but that only matters if the fight goes on for days. Conan has fought long enough to know to conserve energy, and he’s been in enough one on one duels with people his own size and strength to know the ebb and flow of combat. Captain america is rarely against people of his own caliber. Either he faces a lot of people, all of whom are worse than him, or he faces people who are big enough to manhandle him easily. Conan will fight Captain America toe to toe, and thats not something he’s used to.

A shield… Its just not as effective a weapon as an Axe, or a sword, or a spear, or any other weapon Conan uses with equal amusement. I don’t care how good you are with it, a shield is for defence and surprise attacks. If you go into battle with only a shield and your fists, and the other guy has a Weapon capable of tearing through your spandex, you’re a dead man.

Methinks Conan’s weapons would break on Caps shield.
A shield throw could end the match.

“The Spartans suggest other wise on the sheild not being an effective weapon.”

No they didn’t. if they would have argued that they would have not taken swords, spears and the like. Maybe another shield instead. A shield is at its most basic level a Defensive weapon.

“What? So Red Skull,Baron Zemo,Taskmaster,Bullseye,Crossbones and many others are not on Caps caliber?”

Bullseye, no. He’s a well trained and impeccably accurate merc. Hardly a supersoldier, but he stands toe to toe with cap and occasionally, if not wins, at least forces him back.

“On the subject of the shield,you’re kinda’ downplaying it don’t you think? It’s an unbreakable shield which has taken blows from guys like the Hulk. Cappy could end Conans life with one well-aimed toss.”

So could archers, spear throwers, and a dozen other long ranged killers. Weirdly though, Conan knows to avoid projectiles. Even a shield, which is generaly a very odd thing to be seen thrown, is known to him to be painful and therefore he’s going to dodge.

It boomeranging on his could cause some issue, but by then he’ll have responded in kind. And with cap dodging, his shields not going to be going right back to him, because he might not be where he thought he would be.

I seem to remember hearing somewhere that in a crossover between these two that Conan beat Captain America. However I myself have never read that crossover and would put my money on Cap.

Catain America : Pow! Right in the kisser

Cap wins
but his uniform isn’t spandex it is micro chain mail (or at least in places)

At SS: Winning post right there. A modern gun with an unbreakable shield can easily overcome any primative weapon. And avoiding a gun shot is much harder then avoiding an arrow, especially if you never seen one.

Capt. America for the win.

“…This match is under duels and not swordfighters isn’t it…

Damn it all, Guns ruin the fun of these epic matches/”

Well, on Factpile we do use current incarnation, then Current Captain does use a ballistic weapon (gun). Sorry Connan, but gun crushes him.

- the pondering fool

@Jwlynas
well the original cap used a gun too, but only in the war

OK. Conan is likely the mightiest warrior that’s ever walked the earth. He eats for breakfast, beasts that the Captain would run in terror from. He’s faaaar from normal. This guy defeats gods and beasts in single combat every day of the week (except Sundays). I love Captain America, but to Conan he’s just another gladiator dressed in blue.