Could go either way from what we've seen so far from both guys.
They both have impressive feats of archery, from being able to hit moving tennis(the tennis balls were'nt going to fast butstill very impressive) balls to not even having to look at their target to hit a bullseye.
Figured this would fight would pop up eventually. I'm leaning towrds Hawkeye mainly because he appeared to have better skills with a bow (the no-look one shot was impressive and beats anything GA has done with his bow so far) and he actually had trick arrows...I do think GA is a better fighter tho, so if it came to h2h he might have the edge. We really need to see more from Hawkeye in the h2h dept