In wireless communication systems, accurate Channel State Information (CSI) is essential for base stations to perform downlink precoding. While much of the existing research primarily focus on compressing the CSI matrix, they often neglect the impact of subsequent pre-transmission processes such as quantization, channel coding, and modulation. This paper investigates two distinct approaches for CSI dimensionality reduction: TransNet, a transformer-based neural network, and Dynamic Mode Decomposition (DMD), a mathematical decomposition technique for dynamical systems. We analyze how quantization, channel coding, and modulation affect CSI feedback for both methods. Unlike TransNet, DMD can decompose the channel matrix into components (called modes) with varying significance. This decomposition allows for an effective application of Unequal Error Protection (UEP) techniques to DMD modes, which is not feasible with TransNet-based CSI. Simulation results reveal that while the compression performance of TransNet and DMD varies based on factors like target CSI size and channel estimation error, integrating UEP techniques for DMD-based CSI yields superior CSI transmission performance compared to TransNet-based CSI.