Chief can toss a coin, tell you what face it'll land on, and punch it before it hits the ground. Cap may be old and battle hardened but John would outlast, outskill, and overpower cap. The only argument to be made for cap is his shield which can take a blow from anything the chief can muster but would surely be torn out of cap's hands by the chief superior strength, especially taking in to account his experience with jackals.
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The only advantage is that Chief is 3X stronger in Mjolnir armor. Otherwise Cap has him at every other stat. He's just as fas, just a durable, and is a better one on one fighter. Chief isn't the first stronger opponent he's squared off against. Cap has gone toe to toe with the Hulk and lived to tell about it.