Cellular-connected unmanned aerial vehicles (UAVs) are recently getting significant attention due to various practical use cases, e.g., surveillance, data gathering, purchase delivery, among other applications. Since UAVs are low power nodes, energy and spectral efficient communication is of paramount importance. To that end, multiple access (MA) schemes can play an important role in achieving high energy efficiency and spectral efficiency. In this work, we introduce rate-splitting MA (RSMA) and non-orthogonal MA (NOMA) schemes in a cellular-connected UAV network. In particular, we investigate the energy efficiency of the RSMA and NOMA schemes in a millimeter wave (mmWave) downlink transmission scenario. Furthermore, we optimize precoding vectors of both the schemes by explicitly taking into account the 3GPP antenna propagation patterns. The numerical results for this realistic transmission scheme indicate that RSMA is superior to NOMA in terms of overall energy efficiency.