Which travels further, a football or a soccer ball, when thrown?
The drag force on an American football is in the range of a coefficient of .05 to .06. If the football is spinning the drag is slightly less.
The drag on a FIFA soccer ball is a coefficient of .25.
The football should travel further. The diameter of an NFL football is about 17.3 centimeters. The diameter of a FIFA soccer ball is roughly 22 centimeters. The greater cross sectional area of the soccer ball creates a thicker wake and more drag, as Sebastian Riese points out in his comment.
The chief difference between the balls, which produces less drag on the NFL football, is the shape. The NFL football's wake is significantly thinner than the soccer ball's, to a great extent because of the shape of the ball. The hulls of ships, for example, are designed like a football's shape below the water line toward the stern in order to allow a more laminar flow as the boundary layer separates from the back of the hull. Laminar flow creates a thinner wake which produces less turbulent viscous drag.
Hmmm - the above answers assume that the american football (I'm a Brit) or rugby ball (they are similar shapes) does not start to tumble in flight. Every rugby player knows to throw a spin pass - ie to impart spin onto to the ball around the long axis while throwing the ball in the direction of the long axis to ensure that the pass stays true - basically emulating the function of rifling in artillery. From what I've seen of American football quarter back play - their passes are thrown similarly - albeit one handed.
Comparing the distance of punts in rugby and association football leads me to wonder whether the football flies further - because of the impact of tumbling but the evidence is inconclusive. There have been soccer goals scored by goal keepers from punts - the first bounce ends up close to the opposition penalty area - that kind of distance for a goalkeeper is relatively commonplace and is about 70m. In rugby, a similar distance is from home 22m to opposition 22m line - a rugby player kicking from inside his 22m line to touch in the opposition 22m area would be a huge asset - and is uncommon from my experience. The distance here might be ~70m (60m from 22 to 22 + an addition for the crossfield element of the kick. The nature of the game would be that such a kick would be aimed to go out of play between 22m and goal. The rules of the game make it less likely that the kick be from outside the 22m line. Rugby players regularly place kick from inside their own half to score "penalties" ~60m. Unlike gridiron - rugby and soccer pitchs do not have defined lengths ~100m within a margin is the rule for both sports.
I am sure some statto will have distances for the longest punts in gridiron - I dont.
In conclusion - long kicks in both Soccer and Rugby are ~70m - imparted by the same implement, the human foot. It would be interesting to see some more conclusive evidence - but that would take experimentation.