This paper explores whether considering alternative domain-specific embeddings to calculate the Fréchet Audio Distance (FAD) metric can help the FAD to correlate better with perceptual ratings of environmental sounds. We used embeddings from VGGish, PANNs, MS-CLAP, L-CLAP, and MERT, which are tailored for either music or environmental sound evaluation. The FAD scores were calculated for sounds from the DCASE 2023 Task 7 dataset. Using perceptual data from the same task, we find that PANNs-WGM-LogMel produces the best correlation between FAD scores and perceptual ratings of both audio quality and perceived fit with a Spearman correlation higher than 0.5. We also find that music-specific embeddings resulted in significantly lower results. Interestingly, VGGish, the embedding used for the original Fréchet calculation, yielded a correlation below 0.1. These results underscore the critical importance of the choice of embedding for the FAD metric design.