I'm not a weapons buff, so I don't know enough about the technical aspects of each weapon to comment on it, but it would seem to me that the effectiveness of a bow in the overall context of a battle comes down to numbers. The vast majority of Henry V's men were archers at Agincourt.
The samurai began life as mounted horse archers, thus making the weapon relatively restricted in use (to those who could afford the horses and training). I cannot vouch for the effectiveness of ashigaru archers. By the period that I am most familiar with, the bow had begun to be replaced by the arquebus, which requires a lot less training to use effectively (point & click).
I'd give this one to the longbow if it was on a battlefield. In a direct, one on one comparison, I wouldn't know.
Japanese horseback archery, or yabusame:
[ame=http://www.youtube.com/watch?v=ywRP725u11k&feature=fvwrel]YouTube - ‪Yabusame - Japanese Mounted Archery[/ame]
The daikyu (large bow) is used on horseback.