Heterochromatin protein 1 (HP1) family proteins are conserved chromatin binding proteins involved in gene silencing, chromosome packaging, and chromosome segregation. These proteins recognize histone H3 lysine 9 methylated tails via their chromodomain and recruit additional ligand proteins with diverse activities through their dimerization domain, the chromoshadow domain. Species that have HP1 proteins possess multiple paralogs that perform non-overlapping roles in vivo. How different HP1 proteins, which are highly conserved, perform different functions is not well understood. Here, we use the two Schizosaccharomyces pombe HP1 paralogs, Swi6 and Chp2, as model systems to compare and contrast their biophysical properties. We find that Swi6 and Chp2 have similar dimerization and oligomerization equilibria, and that Swi6 binds slightly (~3-fold) more strongly to nucleosomes than Chp2. Furthermore, while Swi6 binding to the H3K9me3 mark is regulated by a previously described auto-inhibition mechanism, the binding of Chp2 to the H3K9me3 mark is not analogously regulated. In the context of chromoshadow domain interactions, we show using a newly identified peptide sequence from the Clr3 histone deacetylase and a previously identified sequence from the protein Shugoshin that the Swi6 chromoshadow domain binds both ligands more strongly than the Chp2. Overall, our findings uncover quantitative differences in how Swi6 and Chp2 interact with nucleosomal and non-nucleosomal ligands and qualitative differences in how their assembly on nucleosomes is regulated. These findings provide a biochemical framework to explain the varied functions of Chp2 and Swi6 in vivo.