As noise pollution remains one of the biggest hurdles posed by thermal engines, increasing efforts are made to alleviate the generation of combustion noise from the early design stage of the chamber. Since the complexity of both modern chamber geometries and the combustion process itself precludes robust analytic solutions, and since the resonant, highly three-dimensional pressure field is difficult to be measured experimentally, focus is put on the numerical modeling of the process. However, in order to optimize the resources devoted to this simulation, an informed decision must be made on which formulations are followed. In this work, the experimental cyclic dispersion of the in-cylinder pressure is analyzed in two typical compression-ignited (CI) and spark-ignited (SI) engines. Acoustic signatures and pressure rise rates (PRRs) are derived from these data, showing how while the preponderance of flame front propagation and dependency of previous cycle in SI engine noise usually calls for multicycle, more complex turbulence modeling such as large Eddy simulation (LES), simpler unsteady Reynolds-averaged Navier-Stokes (URANS) formulations can accurately characterize the more consistent pressure spectra of CI thermal engines, which feature sudden autoignition as the main noise source.