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Who wins

Due to her training on Titan, Moondragon has achieved her full human physical potential. She has trained herself to be as strong as possible for a human being. She is a superb athlete who can surpass the achievements of any Olympic athelete. She has achieved mastery over her body, even over her autonomic functions, like heartbeat, bleeding, and breathing, as well as awareness of pain, althour presumably there are limits to her control. She also has had extensive training in a form of martial arts analogous to Kung-Fu.

Moonie'd give him a fight. I'm leaning towards Batman just because he uses his skills more often. Moondragon works out regularly, but Batman fights daily.

Rick Jones knocked out Moondragon.... then tied her up in his bathroom

Yeah but she went toe to toe against Mantis and held her own.