1) Years of rule changes, and stricter enforcement. Now a top level player who tackles someone above the shoulder, or tackles without attempting to hold on (so no clothes-linse or body checks) will be sent off (which in Rugby is catastrophic to your teams chances). If you lift a player off the ground you are responsible for putting them down again. Drop them on their head and expect a lengthy ban. This hasn't changed the spectacle of Rugby much, if anything the skill levels have improved.
2) Protection. Around your head Rugby only allows you to wear a small soft 'scrum cap' which protects from bruising and wounds from head clashes, like the things boxers suffer with around their eyes. Their is a light collar bone protector which seems to be about 1/5th of the thickness of the equivalent Gridiron gear. That is all. The impacts are still impressive to see, indeed are perhaps more impressive on an un-armoured body, but with lower G-force to the head
3) The size of the people. In both sports their has been an increase in the mass of the players. However US football players seems disproportionately massive. In Rugby their are not rolling substitutions, so you have to carry that mass around for 80 minutes, and therefore a compromise is necessary, perhaps gridiron could restrict the number of subs, or the squad size so the bruisers actually had to run. The miracle of sports nutrition, with the characteristic protruding jaw bones, seem to be producing bigger players than they may if they had effective controls against doping. Yes I said it, from across the pond, it looks like steroid abuse is rife in several US sports.
4) The concussion protocol. Any player that appears to have been knocked out in Rugby gets sent from the pitch to be examined by a doctor for a minimum of 10 minutes. If concussion is detected there is a mandatory period off playing. If concussion recurs this can be months! Welsh International George North suffered repeated concussions and missed most of the following year.
During this same period Rugby has become a tougher sport than ever, but without killing the brains of our young men