The incorporation of source directivity is important for a plausible and authentic auralization. While high-resolution measurement setups and data exist, it is yet not clear how detailed the directivity information has to be measured and reproduced with regard to perception. In particular, when source and listener are at the same location, resulting in a high direct-to-reverberant energy ratio, the precise shape of the directivity pattern might not yield perceptual differences. The paper approaches this question by a listening experiment in a virtual environment with generic directivity patterns and coincident position of listener and source. The experiment compares different spatial resolutions (spherical harmonic orders) of the directivity patterns for multiple virtual listener/source positions/orientations and levels of direct sound for speech and noise. The virtual environment employs a higher-order image-source model and binaural, dynamic Ambisonic playback. The results show that the exact shape of the directivity pattern is often perceptually irrelevant, while the preservation of the direct-to-reverberant energy ratio is more important.