I will provide some statistics so you can decide.
In Rugby Union, on average, a tackle can deal for 1000lb up to 1700lb amount of force. And because of this amount of force, without the protection like in American Football, has a high chance of breaking or fracturing your ribcage. However, on average in American Football the average force is between 3500lb and 4500lb, which, because of the protection, is unlike to break or fracture a bone ( this is dependant on where the tackles hits ). 4500lb is equivalent to 2/3s the power of a car crashing into you. On average, American Football players tackle between 5-7 times a game. However, in Rugby Union, it is on an average of 15-19, doing the math here are the amount of force 1 person deals in a game, for both Rugby Union and American Football.
American Football = 17500lb - 31500lb of force.
Rugby Union = 15000lb - 32300lb of force.
So which do you think is more dangerous, and do you prefer the game where you can inflict more damage, or have a higher chance of breaking bones?