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Who do you think will win this one?

Lady Shiva

Cap's stamina is too high and his stats too great for her to just knock him out. She could kill him, but she couldnt beat him up.

Not if she lands a incredibly complex heart stopping nerve strike or something crazy like that.

Well yeah, but that would be killing him.

Lady Shiva may be a damn good martial artist, but Cap has much more experience, amped stamina, and so on... So i think he would take it.

Captain A does not have more experience than Shiva when it comes to combat. Shiva Woosan spends her life honing her martial skills, and the tests them by challenging the best masters all over the world to matches. Death matches!
And she is still alive!
Cap is a great fighter, and due to the super-soldier serum he is beyond what any human could attain.
But in hand to hand Shiva Woosan would kill Cap.
Not even Batman can face Shiva face to face (the only time Bats won was when Shiva was being mind controlled by Gorilla Grodd, and thus not fighting at her true potential).