Deathstroke would stomp Hawkeye, and Green Arrow was trained in hand to hand combat by the very same man who taught HIM. Captain America is a GOOD hand to hand combatant, but is by no means the best in his universe (that would most likely go to Iron Fist, who knows every martial arts on the planet PLUS other mystical martial arts from Kun'Lun. He also actively holds back when fighting other heroes to make the sparring fair.) Not only that but Green Arrows backstory has been retconned in his "Brightest Day" series to show he has been using a bow since a child (hence why he turned to it on Starfish Island.) His feats include being able to shoot 25 arrows a minute at a leisurely pace, and cutting a water drop in half as it fell from a block away. He also beat Solomon Grundy to death with his bare hands and a broken bow. His. Bare. Hands.
Green Arrow always had "natural skill" with a bow, but despite being a damn prodigy with it he has also backed that advantage up with years upon years upon years of intensive training. He has even been stated to possess an almost "spiritual" connection to his weapon, using it as an extension of himself. While Hawkeye is tough, he is no Oliver Queen. If they ever fought, I imagine that Ollie would be more than happy to teach Clint how to use a bow.
Plain and simple, Clint is outmatched in close combat or from a long range.