ESPN formed a table listing the hardest sports to play and of course due to American ignorance and bias (all those involved were former professionals of one of the major U.S. sports) had soccer at 10th and american football at 3rd. However looking at the figures there is clear bias along with them considering the importance of a characteristic rather than its difficulty within it.

http://sports.espn.go.com/espn/page2/sportSkills

this is what i think the relations should be like:

endurance- Obviously higher than in soccer, more than the 30% or so stated.
power- Of course goes to American football. Not too say they aren't strong soccer players or that strength is unimportant. needed in tussling for the ball, wrestling for headers, shooting, headering, acceleration etc. number given far too low, how is strength more important in the nba?
strength- roughly same as argument for power.
speed- both important but more so in soccer. soccer players also are faster so the numbers again are chosen in favor of American football.
agility- got it right, higher and more important in soccer.
flexibility- in comparison to American football it is far higher, so numbers again bias to American football.
nerves- strange one, risk of injury and fear higher in AF, but nervousness affects the more subtle things in people like a good touch, decision making etc. both occur in both sports, latter more in soccer and former more in AF.
durability- not sure how you measure it but i will give it to AF as in comparison, soccer is not a true contact sport.
co-ordination- Important in both but arguable harder in soccer as using foot, catching and throwing are simpler actions.
analytic aptitude- undoubtedly higher in soccer.

so i have it 6-3 to soccer which I think is fair, gave nerves as equal and unclear. could do same for co-ordination. ESPN even had it as 6-4 to soccer but due to exaggerated numbers meant American football came out on top.

also have to consider the mental aspect of the sport- in AF you are told what to do and do it, do though have to read plays and act accordingly, so not all coaches imagination. in soccer you do not only read the game but aspects like concentration, awareness, vision are more important and higher in soccer. not considering aspects like focus, desire, determination as dependent on players. this could be made to be more in depth but my point is made regardless

finally there is the skill involved- Without a doubt the skill and technique involved in soccer is higher than that of AF. American footballers have limited skills as it is, aside from the QB, and only have to master a few such as catching for instance. physical aspect most important within AF above skill. other way round in soccer, but the relative skill levels to physical aspects high in soccer, meaning the physical requirements are higher than the skill levels needed in AF.

therefore soccer is harder to master, quite simple really.
think of of soccer players, mentally speaking, as all being Qb's aside from the goal keeper, to differing extents.

should add that i do show interest in both sports so this is not me hating.