Some places in USA are super unsafe. The problem in Mexico is you can't trust the police or govt all the time. Also in Mexico they have way more instances of police actually being killers. You don't see that much in the USA.
But trying to sort through stats to say what country safer for the avg citizen is pretty tough to do. I've never been a victim of violent crime in the USA, or my trips long ago to Mexico. I will never be going back to Mexico, but its not because its not safe, just don't want to really. When I go south now I go to my cousins pad in Costa Rica. Only met him once, only been once, but if i go again that is where i will go. He's a hand doctor that had problems in FLA with being blacklisted for tesifying in a trial anout hand surgeries that weren't needed. Guess he should if STFU lol. But he has done well for himself, costa rican wife, sailboat, really nice place in San Jose outskirts where mostly expats live.