Katniss everdeen vs hawkeye (moive versions)

They have both been summoned to a 1 on 1 fight in the arena from the first hunger games moive the only weapons will be bows and arrows and as a special stipulation one has to kill the other in ten days or their loved one dies who wins

Hawkeye impressed me much more than Katniss. More accurate, more skilled.

Hawkeye wins. Absolute slaughterhouse. 
Katniss had trouble hitting a non-moving target consistently when the judges were watching her. Hawkeye casually shot down Chitauri on air speeders without even looking. 
Katniss has serious inhibitions about killing, even when she was in the arena. Hawkeye killed dozens of Chitauri without batting an eye. 
Katniss is a teenage girl with very little formal training, and very little actual combat experience. Hawkeye is a high-ranking heavily trained and experienced SHIELD operative. 
 
This might as well be Ultimate Spider-Man vs What If? Spider-Man. 
It's not even remotely close.