When kids are playing with all their action figures in the backyard, epic mashups between different universes of characters are inevitable. Darth Vader vs. Superman. Earthworm Jim vs. Megatron. Wonder Woman vs. Captain America. Nothing can stop them. Not copyright law, distribution rights, or the bounds of reason.
Let's suspend all of that here, with the exception of reason, to see who would win in a knockdown, drag-out fight between the Amazonian princess Wonder Woman, and the Star-Spangled warrior Captain America. This would be a tough fight without question, but maybe not as tough as fans would think.
10 Captain America: Leader
Captain America's greatest superpower may be one that has nothing to do with the super serum that gave him his strength and endurance. His ability to lead and inspire, which he's done countless times through one crisis after another, motivates others to dig deep and rally when the chips are down. This is critical in a fight against anyone, but especially against Wonder Woman. As will become obvious, Steve Rogers has some deficits when it comes to matching up with Diana, and he'll need all the help he can get.
9 Wonder Woman: Lasso of Truth
Wonder Woman presents a challenge with just her bare hands, so giving her any kind of weapon is kind of not fair. But the fact remains she has them, and the most significant one is the Lasso of Truth. Diana's signature weapon is famous for its ability to squeeze confessions out of people. All it would net out of Captain America likely would be is reticence to fight her. But the lasso also imposes its will on people, and Wonder Woman could use it to force Captain America out of the fight really fast.
8 Captain America: Tactician
One advantage Steve Rogers has is a brilliant strategic mind. His experience in World War II, to say nothing of the considerable time he has spent studying military strategy, history and tactics, make him a significant opponent. He has studied and is an expert in numerous forms of martial arts, making him one of the most impressive hand-to-hand combatants in the Marvel universe. His knowledge and leadership abilities have regularly placed him at the head of the Avengers and other large assemblies of superheroes, including Secret Wars.
7 Wonder Woman: Super Fast
This is where things start to break down for the First Avenger. Wonder Woman's powerset is, to say the least, considerable. One aspect of it is that she's super fast. Diana possesses the Speed of Hermes, which sounds about as wow as it actually is. The Flash can certainly attest to it, even though he's a bit faster.
Wonder Woman can keep with the Flash enough to make Captain America look like he's jogging through the mud. All the inspirational speeches and strategies in the world wouldn't be able to catch up with a punch she throws at MACH speed (or a clothesline, which she's been known to do).
6 Captain America: The Shield
Captain America's best defense in any situation is generally his shield. Made out a virtually indestructible vibranium steel alloy, Wonder Woman would have a hard time getting through it. The shield can be broken and has been in both the comics and films, but it's powerful enough to withstand the might and power of beings that are equal to or maybe even greater than Diana. The shield has protected Captain America from Thor's hammer, the Hulk's rage, and Wolverine's claws. Certainly, it can take a hit from Wonder Woman, and it would have to take a lot to stop her.
5 Wonder Woman: Doesn't Need A Shield
Captain America could punch Wonder Woman all day long and never make a dent. He also wouldn't want to throw his shield at her. That would be bad. Diana is physically super durable to the point she's invulnerable. She's proved that time and again. All anyone really needs to know about it is she can take a punch from Superman. Captain America would not be able to take a punch from the Man of Steel. His shield likely would not be able to, though it could probably fend off the heat vision. But that's Kal-El. Cap is fighting Wonder Woman, and needless to say, it's not going well.
4 Captain America: He's Worthy
The shield might not last long, but Captain America's honesty, integrity, and spirit make him one of the few people worthy to lift Mjolnir, Thor's mystical and powerful hammer. In a pinch, Captain America could find himself in possession of the hammer and things change dramatically in the equation. Mjolnir evens a lot of fights, which is to be expected, considering it can smash planets to smithereens. Steve Rogers could likely summon enough lightning to make the fight competitive against Diana. There's just one problem.
3 Wonder Woman: Godkiller
Wonder Woman absolutely doesn't need weapons against the majority of her opponents, but if Captain America is going to whip out a mystical hammer, then she's going to draw the Godkiller sword. It does exactly what it says on the box (probably didn't come in a box though): it kills gods.
Steve Rogers isn't a god but with the hammer he would be in the neighborhood. Invulnerable, super-fast, and super strong, with a single swing of the Godkiller sword, Diana ends the fight and probably severs diplomatic ties between America and Themiscyra for good.
2 Captain America: Whatever It Takes
At the end of the day, what Captain America has more than anything is grit. When the chips are down - and they're usually down for the Avengers it seems like - he keeps going. And going. That determination carries him forward against the most overwhelming odds and it would be his best asset in the fight against Wonder Woman. Unafraid and unwavering, Captain America battles hard and true to the very end like the soldier that he is. And then she beats him. Because she was always going to beat him.
1 Wonder Woman: She's A God
A good metric to judge this fight by is the fact that Captain America strains to hold on to a helicopter. Wonder Woman lifted a tank over her head and threw it at somebody. That pretty much begins and ends the fight, but if there was any doubt, Diana is essentially a god. The daughter of Queen Hippolyta and the Greek God Zeus, she's vested with power beyond any Captain America could hope to defend. He would do enough to make it interesting, but the battle lasts as long as Wonder Woman wants it to.