Just to add some help for some of the non-American folks (since it'll probably get skipped over after this goes another page or two):
As a few people have already posted, the pads are pretty much needed in American Football. Hits get down-right vicious. The lineman don't get to lock together nicely before they start mauling each other. And there's nothing saying you can't absolutely smear the guy holding the ball into the ground just because he wasn't looking (so long as you avoid some hits, like helmet-to-helmet that leads to some pretty serious medical problems). Sometimes, you can even level someone when they don't have it--case in point is the Option play: the quarterback runs a sweep to a side, with the option of pitching it to someone running a pattern to take it or keep it himself depending on how he reads the defense. On that play, it's perfectly legal for a defensiveman already committed to tackling the quarterback to still take him out even after he pitches the ball. And I've watched it break ribs through the pads in one of my high school games.
Also saw a quarterback's femur get snapped in half. Chased him right into two our our 110kg linebackers. One wound up under his leg. Other on top. But, that's something that could probably happen in Rugby pretty easily, too.
As for the fitness parts of the game, they really don't compare. I played Soccer myself until the eighth grade when I switched over to American Football. My first two-a-days practice, I was running circles around everyone. After the first set of "grueling" conditioning drills, the whole team was huffing, puffing, and spraying themselves with water to cool off while I was bouncing about, anxious to get back to it wondering why everyone was tired after such easy drills. And why not? Years of Soccer, running for miles each practice, and I was nothing but runner's muscle. When it came to actual technique drills, I was horribly weak. During the next summer's 'optional' thrice-weekly lifting and conditioning practices, I put on literally fifty pounds. I was more and more winded each year's two-a-days thereafter, but by transitioning to sprinter's muscle I became one of the best lineman on the team.