The symbiosis between cnidarian hosts and microalgae of the genus Symbiodinium provides the foundation of coral reefs in oligotrophic waters. Understanding the nutrient-exchange between these partners is key to identifying the fundamental mechanisms behind this symbiosis, yet has proven difficult given the endosymbiotic nature of this relationship. In this study, we investigated the respective contribution of host and symbiont to carbon and nitrogen assimilation in the coral model anemone Aiptaisa. For this, we combined traditional measurements with nanoscale secondary ion mass spectrometry (NanoSIMS) and stable isotope labeling to investigate patterns of nutrient uptake and translocation both at the organismal scale and at the cellular scale. Our results show that the rate of carbon and nitrogen assimilation in Aiptasia depends on the identity of the host and the symbiont. NanoSIMS analysis confirmed that both host and symbiont incorporated carbon and nitrogen into their cells, implying a rapid uptake and cycling of nutrients in this symbiotic relationship. Gross carbon fixation was highest in Aiptasia associated with their native Symbiodinium communities. However, differences in fixation rates were only reflected in the δ13C enrichment of the cnidarian host, whereas the algal symbiont showed stable enrichment levels regardless of host identity. Thereby, our results point toward a "selfish" character of the cnidarian-Symbiodinium association in which both partners directly compete for available resources. Consequently, this symbiosis may be inherently instable and highly susceptible to environmental change. While questions remain regarding the underlying cellular controls of nutrient exchange and the nature of metabolites involved, the approach outlined in this study constitutes a powerful toolset to address these questions.