I've played quite a bit of both US (Gridiron) and Rugby (Union) football, and where there are some superficial and historical similarities, it pretty much stops there. 1) Gear. Helmets & pads are necessary for the "full stop" tackles in US football- it's often a game of inches, whereas in Rugby, the thing is posession, which is more flowing. Some "soft" armor is now permitted in Rugby (scrum caps & soft shoulder padding) and, while good for safety, has raised some concerns that this "yank crap" will lead to more dangerous play.
2) Support. In US Football, your support is in front of you. In Rugby, your support is behind you. Sound simple, but it's hard to unlearn hardwired instincts when switching sports. Trust me on this one ;)
3) Conditioning. A lineman is US football can be 6'6" or more and weigh in excess of 300 lbs. They're not much for endurance, but they move with explosive speed and power and are as quick as cats. They are often unnaturally strong and absorb literally bone-crushing impacts over and over. Conversely, a Rugby forward while nearly as large, must be able to stay on the pitch for a full 80 minutes of running and similar impacts. There's more I could write, but I need to earn my salary here & must get back to work. The only way to speak with any authenticity about the subject is to play both sports somewhat competitively to see the levels of athletisim involved. Both require "toughness". Good discussion. Feel free to PM me.