This paper investigates unmanned aerial vehicle (UAV) data collection systems with different multiple access schemes, where a rotary-wing UAV is dispatched to collect data from multiple ground nodes (GNs). Our goal is to maximize the minimum UAV data collection throughput from GNs for both orthogonal multiple access (OMA) and non-orthogonal multiple access (NOMA) transmission, subject to the energy budgets at both the UAV and GNs, namely \emph{double energy limitations}. 1) For OMA, we propose an efficient algorithm by invoking alternating optimization (AO) method, where each subproblem is alternately solved by applying successive convex approximation (SCA) technique. 2) For NOMA, we first handle subproblems with fixed decoding order using SCA technique. Then, we develop a penalty-based algorithm to solve the decoding order design subproblem. Numerical results show that: i) The proposed algorithms are capable of improving the max-min throughput performance compared with other benchmark schemes; and ii) NOMA yields a higher performance gain than OMA when GNs have sufficient energy.