I think this is mostly the same as my post above.
Cap, like Tony, downscales from Thanos but is arguably higher in AP than Stark is, as he stood a better chance than Stark did. Physically, Cap should be able to overpower Akame in close combat.
Cap definitely isn't higher in terms of AP than Tony, he's only that strong via the hammer. Aside from from he's either comparable or slighty weaker than Tony's armors especially from a range. He had to team up with Bucky to actually even stand a chance against Tony's armor as they kept attacking him and not allowing him to range spam.
However, Cap not being armored leaves him to being vulnerable to Murasame, one hit and it's over for him.
This is true.
Cap does have some advantages. He could simply call in several lightning strikes from a distance.
To which she can dodge via Acrobatics and has experience in avoiding AoE lightning strikes from Budo. Cap also doesn't spam said lightning strikes and is very much inexperienced in using the Hammer unlike Thor.
Throw Mjolnir at Aka me, which she can't defend against,
To which she can just dodge, the Hammer doesn't have a large AoE and has a travel time. Akame can simply leap over it, side step it and so on and so forth. If anything throwing it would be a disadvantage for Akame as that would leave him open for a short period of time.
and use his shield to guard against her attacks, as I doubt he'll sit around and get stabbed.
Akame wouldn't bother attacking the shield, she'd go for more vital areas such as his unprotected face. If he Blocks she can counter by attacking the area where the shield isn't at such as his legs.
He's also significantly older than she is and has been fighting for likely longer than her. He should have comparable if not more experience in combat.
Experience =/= skill. In the skill category neither opponent has the edge as they're both different types of combatants. And MCU Cap is severally lacking in the skill department in comparison to his comic counterparts.
Basically, both can practically one shot each other, but Cap has more advantages to take the win. Cap wins with High difficulty.
I'm gonna have to vote for Akame here, one cut means certain death and with the two being comparable in the skill category it's impossible for MCU Cap to avoid everything Akame can throw at him. Cap can't end the match in one attack, Akame can with a single wound.
I guess him being a comparable fighter and having higher AP combined with sword and hammer range spam. His attacks are very unpredictable and it helps that he's very adapt against swordfighters
MCU Cap doesn't have unpredictable attacks like his comic counterpart. If this were comic Cap I'd have to agree but this is MCU Cap who's shtick is pretty 1 dimensional. Strikes and defense via the shield, perhaps some throws and lightning from the Hammer which he's pretty inexperienced in utilizing. And while MCU Cap has experience in dealing dealing swordsmen Akame can counter swordsmen with Analytical Prediction and character's with mind reading.
TLDR; Akame is vastly more agile, deadly and skilled than MCU Cap in terms of armed combat.