Along with what others have said about the pads possible being part of the problem allowing you to hit harder, there are other factors that contribute to the da

Along with what others have said about the pads possible being part of the problem allowing you to hit harder, there are other factors that contribute to the danger. The American football is played in a series of short plays with long stretches of non-action between plays. This allows plays to be more explosive allowing players run at faster speeds for shorter distances. Also some of the rules lead to greater specialization, which favors some players become much larger (offensive linemen in particular) than rugby players. So the combination of greater mass and greater speed can lead to more dangerous play. At least that's my take on it.