This is actually a debatable topic. The thing is the NFL has finally been forced to reckon with this fact. Hence all the rule changes that your crazy, redneck, right wing uncle hates.
It's a sport that's over a century old with a PLAYER'S UNION and the vets are entitled to pension and health care. MMA as an organized sport is very young. No union for the fighters. I would expect many more fighters down the road to have really bad outcomes.
Here's another point. When a football player has a concussion, the opponents don't keep hitting him when they go down. Mario Yamasaki has taken years, if not decades off of some fighters lives.
They're both dangerous and it depends on the position for the NFL and fight style for MMA fighters. I'd say overall, MMA is more dangerous nowadays. Once the UFC cuts you, you're on your own, whereas the NFL at least has some form of long term health care. The NFL is at least trying to address the problems, while Dana has hookers snorting lines off his cock.