In this paper, we characterize the energy efficiencies of two important spectrum sharing paradigms, namely the interweave based spectrum sharing (ISS) and the underlay based spectrum sharing (USS). We demonstrate that although USS can have higher spectral efficiencies than the ISS, the USS suffers from poor energy efficiency. The primary reason for this is shown to be use of excessive power for small rate gain for the unlicensed or the secondary user (SU) in the USS. On the other hand, if the spectrum sensing errors are kept in control in the ISS, the SU achieves most of its communications through interference free transmissions and consequently utilizes less power to transmit more, thereby being energy efficient. © 2019 IEEE.