I'll try to do this honestly, even though I hate soccer.
Hand-Eye Coordination: Soccer
Most soccer players have very high-eye coordination and have to juggle a ball with feet, knees, and head without using their hands. That's pretty hard to do. I believe it's much easier for someone to catch a football than to manage a soccer ball. Anybody can catch football to be honest, it's not hard. Especially when you compared them to Offensive Tackles/ Defensive Lineman, all you have to do is block somebody and being 6,5 344 pds., how hard can that be...?
Physical Strength: Football
What other sport demands more physical strength and toughness than football. It's a demolition sport with human body parts.
What's one of things college/pro scouts emphasize the most, before they even think about drafting a player...how fast he is...?
Team Work: Push (both sports are great at it.)
A team's success is probably most important thing in both of these sports, and even more so than all other team sports. Unlike (pro) basketball and sometimes hockey, one or two s great player cannot get you to the playoffs. You need a good all round team to succeed in both sports. There's too much going in the course of the game for one player to sit around and look. You have to know wear your teammates are going or what plays they are running.
You can't do too much isolation.
Agility: Soccer (controversial)
Most football players are super agile, being able to move backwards and fowards at high speeds and move well from side line to sideline, but have to give the edge to soccer players.
In football, even though players play on big field, the game has been played in a kind of box. If you watch most football games, the pace can be very slow, since the players stop after each play and offense cannot score or make big plays unless the (big guys) offensive line has enough time to set.
Until recently, football has become more wide open, because of the reliance on having a great passing attack, which can speed the game up but at the same time. The best football is played with simple bruise and bash the other team.
In soccer, the game is a constant flow, there is rarely any stoppage, as the players constantly move from side to side and up and down a really huge field, all while having to juggle a small ball without your hands.
And naturally, they would be much more agile than football players, because their much smaller and slippery.
Size: Football players (by far)
Another thing, scouts look for is how large someone is, even though size don't always equate to talent. It can give some players a certain advantage over others.
Size is obsolete in soccer. You can be almost four feet tall and be stud in soccer (because of great skill). In football, you'd probably be just water/towel boy or something.
I think that the NFL players would win in most events or contests, but I think the soccer players might put up fight in the skill competitions, and maybe some of the speed ones.
Soccer is not a sport, where someone can just pick up and play, it very hard sport to learn. It's something that might take few years to play, because have to have great control over you body.