The tackling in both games is different.
For one, the helmets protect them from tackles that hit above the neck, which are legal in American football, where as they're not in rugby. Spear tackles are also legal, which aren't in rugby, and the force behind one of them whilst running at full speed is bloody hard! I'd like to see you chase a ball that's been thrown long, without any pads, as a tank of a man sprints the other way directly towards you with the intention of spearing you in the chest head on. It's not like rugby, you don't already have the ball in your hands, and you can't just pitch it off to the side to avoid a hit. You either get past, or take the hit.
In American football you're also allowed to take down players without the ball, which you can't do in rugby.
Personally I prefer American football. Some people struggle to enjoy it due to it being quite stop/start, which is fair enough, but I prefer the strategy and skill involved in it that doesn't exist so much in rugby. The plays, the throwing and catching etc. The way that in rugby you can't pass forwards has always put me off it. In American football it's so satisfying when a quarterback throws a huge 50 yard touchdown pass!