As a man who has played American Football as an Outside Linebacker (left side), and a man who has played Rugby a tighthead prop, I can assure you, Rugby is harder.
I have broken ribs, ruptured both kidneys (hence needing a transplant), bruised my liver, and fractured my collarbone in Rugby. After a good game, I would ache for a few days.
After a game of American Football, I could walk without pain, was barely winded, and hardly scratched.
And really? Do you see honestly see any NFL player having the slightest chance of going for the full eighty minutes? Without a breather after every tackle and without endless substitutions? These guys have spent a lifetime training for a sport played in 5 second bursts, and they are great for those five seconds. But cardio is not exactly high on their training priorities list.
And do you really see any NFL runner coping with an offense where there is no blocking and offloading during the tackle is utterly critical to run a successful offense. Bo Jackson might be great -- until he went down. Then it would be a turnover every time as he would have absolutely no offloading skills.
The fact of the matter is that both sports are so completely different -- and take a lifetime of training to compete at an elite level -- that each team would be utterly hopeless at the other sport. Forget the All-Blacks. Any fourth-level English semi-pro club would crush the Packers in a rugby match. As would any Division III NCAA college team crush the All-Blacks at American football should they find themselves on a gridiron pitch.
So my question is why compare rugby and gridiron? You might as well choose basketball and ice hockey. It makes as much sense.
If you were to have an intermediate sport, Australian rules Football is probably the best way to go, half rules of Rugby, half rules of NFL, the brutality of both sets of tackling.