A Gracie practitioner once told me that he felt MMA was safer than boxing for the competitors' long-term health. His explanation was that boxing matches typically run much longer and involve many more head strikes per match than MMA matches, which means the boxers are more at risk for brain damage.
This was also part of the UFC's argument to help regulate MMA. They kept a small number of rounds, a point system, and refs who could call a match when someone stopped protecting themselves. This, along with no strikes to the back of the head, made UFC on average more safe than boxing (unless you get head kicked, in which case you're definitely worse off).
