This publication investigates the performance of demodulation methods utilized in spread spectrum chaotic communication systems in order to understand conditions at which advanced demodulation methods, such as chaotic synchronization, provide tangible benefits over classical, matched filtering-based approaches. We conduct simulations and comparisons of three different communication systems: classic direct sequence spread spectrum (DSSS), chaotic signal fragment-based pseudo-chaotic spread spectrum (PCSS), and chaotic synchronization-based antipodal chaos shift keying (ACSK). These systems possess similar spectral and time domain characteristics, allowing us to shed light on their fundamental differences and limitations in chaos-based communication. Additionally, we assess the impact of frequency modulation (FM) on these modulation methods, as FM allows the creation of simplified non-coherent modulation schemes. Our findings, based on the analysis of bit error ratio (BER) curves, demonstrate that in the case of a non-dispersive communication channel, the utilization of chaotic synchronization does not allow to achieve performance of correlation-based receivers. Additionally, the utilization of chaotic synchronization for multiple access poses certain challenges due to malicious synchronization between users. As a supplementary finding, we show that in systems with matched filter-based demodulation, discrete-time quantized spreading sequences confer an advantage over analogous, continuous-time spreading waveforms.