This study deals with the comparison of different numerical fidelity levels to predict the noise of an isolated propeller in positive and negative thrust conditions. For this purpose, unsteady Reynolds-Averaged Navier-Stokes (URANS) and Improved Delayed Detached-Eddy Simulations (IDDES) were carried out and compared with Lattice Boltzmann (LBM) very large eddy simulations and wind tunnel data measured at TU Delft. It was found that the aerodynamic behavior with respect to the propeller loads, flow field in the slipstream, and surface pressure was well predicted by all methods. In the subsequent acoustic propagation, according to the Ffowcs Williams - Hawkings analogy, it was found that the noise directivity differed when using different CFD methods for the case of negative thrust due to increased broadband noise, while all CFD methods showed a similar noise directivity at the first blade passing frequency in the positive thrust condition. In the negative regime, the URANS simulation did not take into account the broadband fluctuations, which led to a significant underestimation of about 40 dB in streamwise directions in the overall noise, while IDDES and LBM showed similar trends, but still deviated about 5 dB in the prediction of the overall noise. Finally, a study was conducted with a low-fidelity acoustic evaluation based on Hanson’s model, which enabled a direct comparison of noise generated only by propeller loads, where a good agreement in tonal noise was achieved compared to the FW-H formulation with all CFD methods exhibit a similar noise directivity in both operation conditions.