This work deals with multi-level switching amplifiers, in the context of high-efficiency power amplification for signal tracking applications. In particular, this paper evaluates the reduction in the error signal's power due to multi-level power amplification (compared to conventional two-level amplifiers) and compares the performance of two multi-level pulse modulations: PWM and Asynchronous ${{Sigma}} {{Delta}}$ Modulation. First the intrinsic bandwidth limits of multi-level switching amplifiers are inferred, to clearly state the advantages and limitations of multi-level power amplification. From the existing analyses of Pulse Width Modulation already reported in the literature, PWM is herein extended to multiple levels based on an equivalent representation, which allows to derive a closed expression for the power spectrum of multi-level PWM in bandlimited signal tracking. The Asynchronous ${{Sigma}} {{Delta}}$ Modulation is extended to multiple levels and the resulting multi-level encoding algorithm is analyzed in both time and frequency domains. The performance of both modulations is characterized and compared at different operating frequencies and using different number of levels. The main outcomes of this in-depth characterization show that, if the switching frequency is high enough, the tracking error is independent of the modulation and the switching frequency, i.e., it only depends upon the number of levels, which points out the suitability of asynchronous modulations for relatively low switching frequencies (compared to the number of levels).