I will repeat...they are all different games...its like asking which is better, bowls or curling...
Rugby requires intense cardio and the ability to take big hits and carry on.
NFL requires intense short bursts with the knowledge you will go down somehow.
With the padding the NFL requires, the hits are more wreckless, however when I played as an outside linebacker, i would drive with my shoulder or head knowing it wouldnt hurt me but may hurt him and I wont have a concussion or injury after.
When I was a prop in rugby, if Ibdid the same sort of tackles, I would have been sent off for unsportsmanlike conduct, dangerous tackles and would have definitely injured myself.
Because of how the games are done through the school system in both countries, in the US a school tends to focus on one main sport with the other events taking second place, whether the main sport is american football, basketball, swimming etc.
In Europe they tend to give all sports a fair chance. Football (soccer), rugby, hockey, cricket, track and field.
If in Europe the education regime plowed the money into sports the same way the US does (high school and college/university level) then you would find the level of the sport would be elevated higher.
In the UK at least (and Germany) a large focus is on Football, and in the UK (except England) rugby IS the national sport - Scotland, Wales, Northern Ireland and Eire.