You can't just insert a soccer player into an NFL game. They're not strong enough or, gasp, fast enough to survive. They're not trained for it. Likewise, an NFL player, no matter how fit, would not do well in a soccer game. They're not trained for it, either.
It's ludicrous to judge either sport on the size or speed of its players. The objectives of each game are different, and so the players develop their skills and bodies accordingly.
Nail on the head there man, the sports are indeed completely different. It is very hard indeed for either side to convince one another that either is "better" than the other simply because they appeal to completely different people often with completely different backgrounds.
Americans (for the most part) live, breathe, and die football from the time they are born until the time they die (I assume the same for soccer fans across the pond). I see babies being rolled around all dressed up in Detroit Lions gear all the time (no matter how much our team sucks), same goes for so many college teams (Michigan, Ohio State, and Michigan State take the cake around here), and even some high-schools (Forest Hills Central, Rockford, and East Grand Rapids are popular here).
...We are trained to play football throughout school, and teams are formed as early as 5th or 6th grades, and often times, those players go on to become the Tom Bradys and Tiki Barbers of the world. It isn't that we don't like soccer (I played it quite a lot as a child, and have recently gotten back into it), it just isn't a part of the collective sporting landscape of the country as football or baseball is.
IMO, I have a harder time playing football as compared to soccer for a few different reasons. First is that I really am not good at catching many things. Secondly, once hike is called, plays can become increasingly hectic, and nearly seems like "every man for himself" until points can be scored. Normally I am cast either as a running back or a offensive lineman (occasionally a corner back, but that is a rare occurance) if I play, simply because of my size (little over 6ft, 160-ish lbs) and speed. When hike is called, I may over-persue the man in possession of the ball, not move fast enough for a carry, etc... My reaction times are often just a bit "off" compared to the rest of the football-playing crowd.
Soccer comes a bit easier overall, however my playing style is a bit more slow and relaxed compared to most players. What I do like about soccer is the "open" feeling to the field, as it allows for a better view of who is doing what, and where I may need to go to get the job done.