This paper investigates the relevance of numerically simulated head-related transfer functions (HRTFs) for the perceived authenticity, plausibility, localization accuracy, and immersion in music-related virtual environments. For this purpose, personalized HRTFs were created for 46 individuals using a 3D scan of the head and torso. Numerical calculations were performed with the Mesh2HRTF library, using the fast-multipole BEM solver to generate the HRTFs. The subjects had to evaluate jazz and classical pieces played by musicians in a virtual concert hall when using the personalized HRTF, a generic HRTF (KEMAR) and a simplified personalized HRTF. Additionally, the influence of music preference and musical sophistication was measured. The results of mixed factorial repeated measures analyses of variance showed that, compared to the other two HRTFs, the personalized HRTF statistically significantly improves perceived immersion, plausibility, and localization accuracy for the participant group with a high musical sophistication score, contrary to the group with a low musical sophistication score. No effect of musical preference was found. Individuals with a high degree of musical sophistication thus seem to benefit particularly from the personalized HRTFs, regardless of the genre of music and individual music preferences.