Captain America stomps. He consistently hurts or even KOs class100 opponents such as Rhino, Hulk, or Thor. He destroys entire teams of powerful villains such as the U-Foes. Kraven doesn't stand a chance.
Multiply all of Kraven's abilities by three or four and what do you get? Someone along the lines of Warpath maybe (of the X-men/X-force). And what happens when Captain America faces off with Warpath? Warpath goes down in less than a second, too fast for the writers/artists to even bother depicting that on-panel.