The paper presents a comparison of phase-shifted and modified level-shifted carrier-based PWM strategies for a three-level H-bridge flying capacitor converter. While the optimal voltage quality of the nearest level switching may be obtained using both of them, natural voltage balancing dynamics is different. Using elementary circuit theory and switched system time domain analysis, it is possible to obtain simple analytical averaged voltage balancing dynamics solutions. Modified level-shifted carrier-based PWM is shown to provide much faster voltage balancing dynamics, especially, for small DC PWM voltage commands and AC PWM modulation indices. The explanation of this fact is obtained by analysis of zero voltage state sequences for different modulation strategies. Relatively fast voltage balancing dynamics rate provided by modified level-shifted carrier-based PWM for zero voltage command makes it possible to implement simple flying capacitors self-precharge procedure at power-up.