I think part of that is the fact that in fighting you have that laid right out there in front of you; the athlete knows the objective is to cause head trauma and participation means they're at the risk of it. Which is of course why much less people choose MMA or Boxing than football. And typically youth aren't going to be able to go full contact until they're near an adult age unlike other sports. Also in both sports after a knockout they receive extended medical leave, sometimes of over 3 months in which they can not go to the gym and spar. I think in general since the risk is more obvious there is more attention to the medical condition of the fighters, and more caution in how they treat them than in football where players get concussed then are back in practice a couple days later.
Also, I do think that while MMA has some brutal fights for the most part the lack of full gloves and standing counts causes fights to end faster and lower the rate of excess damage after sustaining a concussion. The problem is if the ref is terrible that goes right out the window and may make it even more dangerous. Which played a big part in the only time a fighter has ever died as a result of what happened in the cage.