In this paper, we compare the energy efficiencies of two well-known transmission schemes that can adapt to fading channels for reliable transmissions, namely, adaptive modulation and coding (AMC) and hybrid automatic repeat request (HARQ) schemes, with limited channel state information (CSI) feedback. Since they exploit CSI differently, they have different characteristics, which make the comparison study (in terms of energy efficiency) challenging. Using the notion of energy-delay tradeoff (EDT), we derive approaches to compare them with given equivalent quality-of-service (QoS) constraints. The derived approaches are important as they allow us to choose energy-efficient transmission schemes under certain conditions. It is shown that AMC is more energy efficient than HARQ with incremental redundancy (HARQ-IR) in the low-power regime. However, in the high-power regime, HARQ-IR has better energy efficiency than AMC.