If I had to guess, I'd say disparity is more relevant than poverty outside of 'fringe cases'. I'm basing this purely on my idea of common sense, so make of that what you will. The basis for that opinion derives from my opinions for what drives culture, which is fundamentally sex. To be blunt and extremely politically incorrect, a guy is only worth what he brings to the table *compared to other options for mating*. Hence, if a guy is competing with men who make much more money than him, he has to be more fanatical in his behavior to stand out.

That's my guess and I'd be surprised if the numbers didn't back that up somewhat. That means according to Valg's Gini index, there would be a higher crime rate in countries with an index between 40 and 60 than those between 0 & 40 and 60 & 100.

The second point of your post is highly relevant too because social engineering influences behavior. In many ways, Americans are 'engineered' in a certain way. Obviously that has to have some bearing on behavior.