I agree with @bane_of_sith completely.
Daredevil pretty much wins. I think that there is somewhat underestimation on his part.
And he has dodged multiple bullets (and is capable of deflecting bullets) at pt. blank range. Why would arrows be more of a problem to dodge?
1.He can fire 10 at a time,DD still has the speed,reflexes,acrobatic ability,etc to dodge it.
2. He has the ability (because of the radar sense) to see any arrows that Hawkeye may try to ricochet (IF he can even do that,since I haven't seen him do that).
3. He stomps Hawkeye in fighting abilities. I know I've said this before,but DD is one of the best fighters in comics (even though Ult. Hawkeye is an amazing h2h combatant,one of the best in the Ultimates team,in my opinion). Ult. Hawkeye doesn't hold a candle up to him. He isn't fighting someone who has the same skill-set as canon fodder,this guy is basically immune to all of his advances.