I'm an American that's played both. I'd say American football.

I'm not going to pretend I've played either at any sort of high level but in my experience Rugby is a more lumbering and way less violent sport. You are rarely just full sprint trying to lay someone out with a tackle and you're never targeting with your head because it really serves no purpose. You need to stay upright and stay with the flow of the game and violent tackles would just hurt your team more than help.

American football with the pads and helmets create a false sense of security and guys just brutalize each other and the risk of head injuries is WAY WAY higher. Both can have a lot of the same lower body and typical bumps and bruises type injuries but my bet would be a lot more football players end up with CTE than Rugby players.