The purpose of District 12 is mining coal and other resources. With a purpose revolving around such filth from the mines, the Capital puts this district in low priority which is why it is the lowest district number. This lowers the attention it gets from the Capital, which lowers the district's status, which then lowers the general wealth it receives, resulting in a heavily stricken area of poverty.
The difference between these two settings can be traced back to the amount of attention each of them gets. The attitude, circumstance, life, and wealth of the overall population of each District are all determined by how much each one is favored and based on a scale of 1 to 12, 12 being the lowest favored, one can easily tell how well their District is favored just by remembering what their District number is.
The purpose of District 1 is to produce the elegant furniture and jewels that all the citizens of the Capital of Panem use. With workers of such skill and craftsmanship where their works are often desired by the Capital, this is why they are placed as District 1. They are the reason why the City of Panem looks the way it does. By being placed as a high priority of the Capital they are provided with much more wealth than other Districts allowing its citizens to indulge in some luxuries only found inside the Capital