Hmm, hard to tell both have great feats. In hand to hand movie cap would wreck movie Logan... But the game changer would be movie Logan's retarded healing factor along with his ferocity. For now Ill give a very slight advantage to movie cap due to him being able to stand up to Logan and defend accordingly via indestructible shield, and also due to the fact that he has excellent h2h skill and him being a technician.
Caps shield swings should knock him out. Sabes put him down, and so did a bullet to the head.. Cap's shield swings can do at least as much damage (More, I'd bet. He cuts through alien armor like it's tissue paper..)
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Also Movie Cap is legit peak human with slight super human feats. while movie wolverine has strength and physical stats of a man. he doesnt even present that much of great skills. the only thing going for him is claws and healing factor and personally i believe Movie Cap will overcome it.
It was either the 2nd or 3rd X-film, wherein a police officer shot Wolvie in the head... I seem to recall him being incapacitated for quite a while before recovering.
I'd imagine that a shield-throw/smack to the head from Cap packs a lot more blunt force than a 9mm round. /shrug
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Movie Cap is superhuman. Way above 2 tones. There was an agents of SHIELD episode where that super powered guy (forgot his name) was running and pushing a huge bulldozer across a field. When he was done he asked Coulson if he managed to beat Roger's record. Phill said "not even close".
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Cap can and will beat on wolverine all day long. He'll never kill him though. He can ko him over and over but wolverine will just keep coming back and back and back until the rare occasions when he does start tagging cap begin to mount up.
So unless you're allowing some mechanism for cap to remove wolvie's healing then this will always end up with cap dead. 10/10 however long it takes.