Both groups have the same ability to avoid murdering someone but not necessarily the same motivation to avoid murdering someone.
If I’m starving and want to steal bread, I have the same ability to choose to steal or not steal bread as someone who is not starving but I MAY have a much stronger motivation to steal the bread. Our motivations are going to be based on what we value. It is possible that I may so highly value obedience that despite my intense hunger I do not steal. In this case, taking the bread may not be theft at all, but you get my point.
The wealthier group has more resources and more to lose by committing crime so they typically have a stronger motivation to NOT commit crime, however they still have the ABILITY to choose to steal, murder etc… if they wish. Likewise, living in a poor area with less resources could be a greater motivation to murder but if someone more highly values righteousness they will more likely choose not to murder. Of course, we have a choice regarding how much value we place on our motivations.
Ultimately, God will be the judge as to who is culpable for their actions and who is not.