Anguillid herpesvirus 1 (AngHV-1) is a pathogen of eels and a member of the genus Cyprinivirus in the family Alloherpesviridae. We have compared the biological and genomic features of different AngHV-1 strains, focusing on their growth kinetics in vitro and genetic content, diversity, and recombination. Comparisons based on three core genes conserved among alloherpesviruses revealed that AngHV-1 exhibits a slower rate of change and less positive selection than other cypriniviruses. We propose that this may be linked to major differences in host species and corresponding epidemiological circumstances. Efforts to derive evolutionary rate estimates for cypriniviruses under various theoretical models were ultimately unrewarding. We highlight the potential value of future collaborative efforts towards generating short-term evolutionary rate estimates based on known sequence sampling dates. Finally, we revealed that there is significantly less genetic diversity in core gene sequences within cyprinivirus species clades compared to species in the family Herpesviridae. This suggests that cyprinivirus species may have undergone much more vigorous purifying selection post species clade divergence. We discuss whether this may be linked to biological and anthropogenic factors or to sampling bias, and we propose that the comparison of short-term evolutionary rates between species may provide further insights into these differences.