Background/Objectives: Staphylococcus aureus isolates from humans and horses of the equine-associated clonal complexes (CCs) CC1 and CC1660 were comparatively investigated for their genomic relationships. Methods: A total of 91 S. aureus isolates (64 human, 27 equine) were subjected to whole-genome sequencing (WGS), sequence analysis, and antimicrobial susceptibility testing. Results: WGS confirmed 75 CC1 and 16 CC1660 isolates, comprising nine sequence types (STs) in CC1 and four STs in CC1660. Ten spa types were present in CC1 and five in CC1660. In the arcC gene of three CC1 isolates, a 285 bp deletion was detected, and a nucleotide deletion causing a premature stop codon was found in one CC1660 isolate. Core genome (cg) MLST revealed a minimum difference of 1398/1492 alleles between the two CCs. All CC1 isolates harbored agr group III and capsule type 8 alleles, whereas all CC1660 isolates had agr group II and capsule type 5 alleles. Antimicrobial susceptibility testing revealed 18 phenotypic and 19 genotypic resistance patterns. All isolates were susceptible to vancomycin, linezolid and quinupristin–dalfopristin. Several virulence genes were detected in different combinations. The equine leukocidin genes lukP/lukQ were found in 22 isolates from horses and 38 isolates from humans, of which 35 had confirmed contact with horses. No Panton–Valentine leukocidin genes were found. Three human CC1660 isolates carried the toxic shock syndrome toxin-1 gene tst-1. Conclusions: The analysis of the 91 isolates might suggest intra- and interspecies transmission among and between humans and horses, which should be monitored in the future.