Well to be honest boxing as a sport hasn't changed much. Football on the other hand, has. Look at the equipment, the size of the players, the speed and strength of the players.
The main point of focus that shows the difference is equipment and style of play. Once again boxing: same as it ever was maybe safer. What are you going to change but the rules (unlikely), gloves, boots, and mouthpieces? Football: more passing, higher impact, and equipment that allows the body to cross pain thresholds it shouldn't. The forward pass was invented to make football safer...it hasn't. It creates 2 vulnerable players the QB and sometimes WR that can be hung out to dry at times. The kickoff and kick return are STILL extremely dangerous and very frightening injuries happen during those. The advances in equipment have done nothing but make players feel invincible and make the game faster...bad combination.

I know I played football and its not a contact sport anymore...its a collision sport.