I guess I feel I should chime in here, having played both sports at reasonably high levels (High school and what we call "cup" teams here in PA and High School and college football for very brief).
First off I think that there are a lot of misconceptions about soccer for those that are unfamiliar with the game in general. I'm not trying to sound like an elitist soccer douche or anything, but when I hear about soccer not being physical or demanding I wonder how I managed to break my nose twice, get four teeth knocked out and break my collar bone, and need a total of about 70 stitches playing such an non-physical sport!
Actually I found soccer to be much, much, more physically demanding than football. Granted, every once in a while, something like what Lavar Arrington did to me in 1993 happens in football: where he hits you so hard you start wondering where you parked the Batmobile -- by the way he did this to me while he was running the ball! - ouch. But honestly those are a rarity, maybe happened to me 5 or 6 times that I really remember. Meanwhile the 90 minutes of constant motion mixed in with mass amounts of sprints all the while trying to keep an eye on the field, players making runs and potential passing routes is very taxing! Not to mention the rough stuff that goes during play. I suggest watching some English Premier League games, if you don't find the game too boring - which is an honest criticism -- Like Reger60 said, I personally find baseball unwatchable, then again that may be because I'm a Pirates fan? But I digress, The EPL is some seriously rough soccer, those guys practically mug each other out there, additionally there is some seriously high quality skill on the field there too, so it's just not all thuggery. It might give a different perspective of the game.
To touch on the subject of soccer preparing you for football -- actually the reason I played soccer is that my father played football growing up and at Pitt, so I always wanted to do what Dad did and play football. I got to the age to start playing Pee-Wee football my dad signed me up for soccer instead, the reason -- he used to work out at a gym that a few Steelers used, he had a conversation with Steve Courson (huge guy, huge steroid user), and he told my Dad to have me play soccer, that you can learn everything they'll teach you in little league football in a weekend: speed, balance and field awareness you can't be taught and soccer does a much better job of preparing you for that. Size and strength come later anyway. Heck, Chad Johnson as much of an oddball as he is, spent most of his life playing soccer, he went into football late in high school because he had more opportunity there.
Ultimately I think that soccer can help out greatly with balance, shifting body weight, transitioning speed from fast to slow and laterally, field awareness and teaching you to mind your peripherals (lose sight of someone for a second and they're behind you with the ball and a great scoring opportunity). Obviously these thing help out everyone and although you do need a fair amount of upper body strength in soccer, football obviously requires more, just like soccer requires more stamina, each sport has it's attributes that require more attention. Overall the skills that can be gained by playing soccer can help out everyone on a football field, more than likely skill positions will be helped out more, especially running back and receivers even great running back don't have the foot movement that a good soccer player has. Simply put you run and react in ways on a soccer field that are more difficult than you typically find in football and being over-prepared never hurts. Guys on the line could also benefit a good bit, the stamina it builds and you can imagine how nice it is to have a big guys with great foot movement a planting ability and balance. Actually as odd as it seems the players soccer really won't help at all is the kicker and punters. The motion for punting is really a lot different that what you do for soccer and place kicking, other than general kicking strength doesn't translate very well either, or the NFL would be awash with ex-pro soccer players.
All in all - the skills from soccer can help greatly although there is a football specific skill set you will have to develop. But the vision and balance and foot skills you can develop will help you in every sport.
