Sorry but I have been to both countries and only in Mexico did the state police with big guns extorted money from me. And that was not a nice experience.
I've lived in Mexico for 20 years. I've been extorted once by police and indeed it's not a pleasant experience.
Having said that, usually I have no issue with police there. Police in the US consistently scares the living shit out of me with their attitude, the way they act, talk, walk... You can see they all feel like the trigger happy gunslinging Sherif in town. Police in Mexico is approachable, have done that countless times. I can't say the same for US police
We used to keep a few cartons of cigarettes in the front of the vehicle to simplify the occasional police shakedown, but that trick was not unique to rural Mexico. It was just as useful in rural parts of Eastern Europe and South America, and basically everywhere in Siberia. It seems power and authority simply don’t age well in isolated regions.