Link adaptation techniques are important modern and future wireless communication systems to cope with quality of service fluctuations in fading channels. These techniques require the knowledge of the channel state obtained with a portion of resources devoted to channel estimation instead of data and updated every coherence time of the process to be tracked. In this paper, we analyze fast and slow adaptive modulation systems with diversity and non-ideal channel estimation under energy constraints. The framework enables to address the following questions: (i) What is the impact of non-ideal channel estimation on fast and slow adaptive modulation systems? (ii) How to define a proper figure of merit which considers both resources dedicated to data and those to channel estimation? (iii) Does fast adaptive always outperform slow adaptive techniques? Our analysis shows that, despite the lower complexity and feedback rate, slow adaptive modulation (SAM) can achieve higher spectral efficiency than fast adaptive modulation (FAM) in the presence of energy constraint, diversity, and non-ideal channel estimation. In addition, SAM satisfies bit error outage requirements also in FAM-denied region.