MMA is safer than boxing.
Boxing when you get knocked down, the ref counts you out and lets you continue even when you’re concussed from getting dropped because some boxers refuse to give up.
In MMA, it’s up to the ref to decide if you were so knocked out cold to decide to stop the fight as a finish.
Also, most of boxing deaths came from brain injuries due to the rules of boxing. Not to mention, more cushioning allows for far more blows to the head. Bare knuckle, while it carves up the face, causes less concussions/head trauma in general.