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Along with spectral efficiency (SE), energy efficiency (EE) is becoming one of the key performance evaluation criteria for communication system. These two criteria, which are conflicting, can be linked through their trade-off. The EE-SE trade-off for the multi-input multi-output (MIMO) Rayleigh fading channel has been accurately approximated in the past but only in the low-SE regime. In this paper, we propose a novel and more generic closed-form approximation of this trade-off which exhibits a greater accuracy for a wider range of SE values and antenna configurations. Our expression has been here utilized for assessing analytically the EE gain of MIMO over single-input single-output (SISO) system for two different types of power consumption models (PCMs): the theoretical PCM, where only the transmit power is considered as consumed power; and a more realistic PCM accounting for the fixed consumed power and amplifier inefficiency. Our analysis unfolds the large mismatch between theoretical and practical MIMO vs. SISO EE gains; the EE gain increases both with the SE and the number of antennas in theory, which indicates that MIMO is a promising EE enabler; whereas it remains small and decreases with the number of transmit antennas when a realistic PCM is considered.