Final answer:
The main controversy between richer and poorer EU members is the cost of caring for refugees, exacerbated by an existing decline in Europe's fertility rate and the resultant economic and social challenges.
Step-by-step explanation:
The controversy between richer and poorer members of the European Union (EU) is most accurately described by option B, the cost of caring for refugees. Richer EU countries are often expected to contribute more in aiding refugees, which has led to tension regarding the distribution of economic responsibility. The influx of refugees, coupled with pre-existing problems such as the decline in the fertility rate and the resulting demographic challenges, stresses the social welfare systems of European nations, creating a divide in opinion on how best to manage these issues.
As Europe is experiencing a low fertility rate, fewer children are being born, leading to an aging workforce and a potential shortage in the labor supply needed to sustain economic growth and fund pension systems. This issue is also tied to cultural tensions arising from immigrants often having different backgrounds from the local populations. Thus, while matters such as the use of the euro, nuclear energy, or even fertility rates play significant roles in the EU dynamics, it is the management of refugees that has sparked recent controversy among member states, especially between richer and poorer countries.