One reason for regional differences are the so called grid fees (Netzentgelte) that have to be payed for by the consumer.
These fees vary in Germany up to around 4 cents per kWh, which is 100 euros for 2500kWh1.
Reasons for varying fees are
Consumer density - The more people there are to share the grid fee, the cheaper it gets for the single consumer.
Age of the grid - The old nets are cheaper to run. In western Germany, more old electricity grids exist compared to the east. In the future, this might change when the power grid in the west will be modernized.
Renewable energies - The expansion of the grid as well as the integration of renewable energies are costly. Furthermore, these sources will often not be fed into the high-voltage power lines1. The lower the load on these power lines, the higher the cost per kWh.
The lower consumer/population density in the north east of Germany leads to a high amount of renewable power generated per consumer/capita (see fig.2 ). Over 7000kWh power are generated per capita in Brandenburg compared to 2400kWh in Rheinland-Pfalz.
1 - https://www.bundesnetzagentur.de/SharedDocs/FAQs/DE/Sachgebiete/Energie/Verbraucher/Energielexikon/Netzentgelt.html
2 - https://www.statistikportal.de/de/bevoelkerung/flaeche-und-bevoelkerung
3 - https://www.foederal-erneuerbar.de/uebersicht/bundeslaender/BW|BY|B|BB|HB|HH|HE|MV|NI|NRW|RLP|SL|SN|ST|SH|TH|D/kategorie/strom/auswahl/175-stromerzeugung_aus_e/#goto_175