In the Marvel universe, the two greatest marksmen are Hawkeye (either Clint Barton or Kate Bishop) and Bullseye. Considering both have been around for over forty years, have they ever faced off in the comics or in other media? If so, who was the victor?
Hawkeye and Bullseye faced off in Hawkeye: Freefall #6.
They seem pretty evenly matched and after breaking several arrows on each other's arrows, Hawkeye used a trick (exploding) arrow and Bullseye was defeated.
They also fought in the Earth-807128 (Old Man Logan) universe in Old Man Hawkeye #9, but it wasn't much of a fair fight. Clint is going blind, versus Bullseye who's had cyber enhancement. Hawkeye is easily defeated by a thrown weapon.