I believe that boxing is by far more dangerous than MMA. The reason is 12 rounds of repeated head punishment, or the ultimate goal for the victor if they can't take their opponent's breath away too easily with the ribs.
A fighter in boxing could get hit in the head, fall to the ropes or even mat, and still have 10 seconds to recover before a KO is called. However, they could still be somewhat concuss, but not showing immediate signs, and continue on to try and get that 1 minute recovery before the next round or before another jab to the head.
Compare that to MMA with a solid knock to the skull that drops a fighter or makes them wobbly in their stance. The ref usually runs in and protects them from a ground attack, calling it then and there, a TKO.
I'm not saying that they can't sustain some pretty serious injuries in MMA, but the match is called when it crosses territory of possible life and death, which I believe only boxing has seen — multiple times — over regulated MMA.
Also the 5 minute rounds in MMA lets fighters take it to the ground or the cage to recover before getting back to pounding or kicking, if they can and aren't just running the clock to go to the scorecard decision.