This study compares noise and signal-to-noise ratio (SNR) in direct detection and coherent detection fiber-based distributed acoustic sensing (DAS) systems. Both detection schemes employ the dynamic analysis of Rayleigh-backscattered light in phase-sensitive optical time-domain reflectometry (ΦOTDR) systems. Through theoretical and experimental analysis, it is determined that for photodetection filters with a sufficiently narrow bandwidth, the SNR performance of both detection schemes is comparable. However, for filters with poor selectivity, coherent detection was found to exhibit superior performance. These findings provide crucial guidelines for the design of high-performance time-domain DAS systems.