This study investigates the relationship between sound quality metrics (SQMs) and noise annoyance caused by airborne wind energy systems (AWESs). In a controlled listening experiment, 75 participants rated their annoyance on the International Commission on Biological Effects of Noise (ICBEN) scale in response to recordings from in-field measurements of two fixed-wing and one soft-wing ground-generation AWES. All recordings were normalized to an equivalent A-weighted sound pressure level of 45 dBA. The results revealed that sharpness was the only SQM predicting participants' annoyance. Fixed-wing kites, characterized by sharper and more tonal and narrowband sound profiles, were rated as more annoying than the soft-wing kite, characterized by higher loudness values. In addition, the effect of some SQMs on annoyance depended on participant characteristics, with loudness having a weaker impact on annoyance for participants familiar with AWESs and tonality having a weaker effect on annoyance for older participants. These findings emphasize the importance of considering psychoacoustic factors in the design and operation of AWESs to reduce noise annoyance.