Having researched it more, they are both equally as dangerous in their own rights.

US football is impact, lots of it, gradual bone crunching above the waist. More tackles as you can hit off the ball and hit most plays.

Rugby is brutal in terms of being stamped on and physical injuries. (see cauliflower ear as an example) You get hit less, but you have no padding.

If there was no padding, American football would have more serious injuries. I think the fact is you need the padding just to play the game.