Rate adaptation and transmission power control in 802.11 WLANs have received a lot of attention from the research community, with most of the proposals aiming at maximising throughput based on network conditions. Considering energy consumption, an implicit assumption is that optimality in throughput implies optimality in energy efficiency, but this assumption has been recently put into question. In this paper, we address via analysis, simulation and experimentation the relation between throughput performance and energy efficiency in multi-rate 802.11 scenarios. We demonstrate the trade-off between these performance figures, confirming that they may not be simultaneously optimised, and analyse their sensitivity towards the energy consumption parameters of the device. We analyse this trade-off in existing rate adaptation with transmission power control algorithms, and discuss how to design novel schemes taking energy consumption into account.