Well I mean it's not rocket science is it. In NFL you wear pads, allowing you to fling yourself around with reckless abandon. In rugby you have no protective gear. In NFL there doesn't seem to be many rules about tackling technique either. When I watch it I often see guys literally just flinging their body/helmet roughly in the direction of the ball-carrier, at the knees, helmet to helmet hits etc. Not to mention you can just annihilate some poor guy in mid-air:
Extremely tough and great to watch, but not exactly safe. In the interests of not crippling our players rugby has rules about how you can tackle. Ie. you have to make an attempt to wrap your arms and can't take a player out in mid-air. Even in rugby league where you could shoulder charge they recently banned it a few years ago. So obviously when you have to mindful of things like that you aren't gonna see big hits as often.
But really...it's just the way the two sports are different. In NFL the players are all spaced out, means guys can get a run up on someone before the smash them. Then you have the nature of the forward pass ie. safeties can just line someone up and blindside them when they are already coming at speed. Plus you get rest after every play, and there is so little actual game time compared to rugby, obviously guys can go all out.
I'd say NFL is more purely violent than rugby, in general the hits tend to be bigger because of everything I just said. Rugby still has big hits, obviously, but in general is more of a grinding, constant physicality with rucks (or hit-ups in rugby league) and
way less breaks.
But if someone is able to read the play perfectly and come out of the line you still get hits like this:
