Race and zip code are equal in terms of disadvantage for those less fortunate.
When it comes to race, those of African American descent will tend to experience more intolerance, disrespect, and racial slurs than those who are not. Similar to those with Hispanic descent in the United States; many people automatically characterize anyone that is Hispanic to be automatically Mexican, rather than, say, Peruvian. Some will go further and claim the individual in question is actually an illegal immigrant.
Similar with zip codes. First off, I live in a reasonably well-off area. My county is fortunate to grace Wikipedia's
top 50 highest personal income counties. I don't notice too much of an issue with zip codes here, but I know for a fact that those people from New York and other prominent areas will tend to sneer at someone who mentions that they are from a lesser prominent area, or perhaps a less wealthy region. Teenagers are much the same. Nocal vs. Socal is one example. My school teems with people who are Aberzombies who insist on wearing Abercrombie, who sometimes scorn people who wear Hollister. I have traveled through certain areas that are not as fortunate in terms of wealth, and I'll be honest: I did shudder at the thought of living in such places.