Computational holography involves creating complex holographic patterns, which is both fundamental and computationally intensive. This process presents significant challenges, particularly in achieving real-time hologram generation. This study presents a thorough comparison and analysis of computational efficiency for computing polygon-based computer-generated holograms (CGH) in terms of programming language (Python and MATLAB), execution hardware (CPU and GPU) and algorithms (interpolation-based and analytical-based). We open-sourced all the codes used for polygonal CGH executed in both MATLAB and Python, offering valuable insights into the performance suitability of different algorithms and languages. Basically, MATLAB demonstrates superior performance over Python, especially for CPU calculations, whereas it performs similarly when utilizing a graphics processing unit (GPU) and an accelerated algorithm like the wavefront recording plane (WRP) method. Analytical-based method and interpolation-based method are not consistently superior; the former performs well when addressing small matrices (e.g., using WRP), while the latter performs well when addressing large matrices.