Both are dangerous but I'm going to go football. I've never heard of half a gymnastics team getting injured in the first week of training. I think football injuries are more common, but gymnastics injuries are often more severe.
I think gymnastics is more dangerous because you are on a beam that is about 2 inches thick and 3 feet off the ground and people do freaking back layouts (in other words a backflip) and back handsprings one after another. In football you have padding and shoulder pads and all that other stuff that protects you, while in gymnastics, gymnasts just wear leotards.