In this work, we present a comprehensive first-principles investigation to compare the phosphates GaPO₄, InPO₄, TlPO₄, and the thiophosphates GaPS₄, InPS₄, Tl₃PS₄, focusing on the [PO₄]^3- and [PS₄]^3- groups. Band structure calculations disclose that TlPO₄ possesses the smallest bandgap (E_g=0.788 eV), whereas InPO₄, GaPS₄, InPS₄ and Tl₃PS₄ exhibit larger bandgaps of 2.604, 2.352, 2.360 and 2.393 eV, respectively. GaPO₄ stands out with its notably large bandgap, which is 4.487 eV. The band structure of the [PS₄]^3- compounds is notably more predictable and adjustable. Density of states analyses indicate that in GaPO₄, InPO₄ and TlPO₄, the valence band maximum is primarily attributed to O-2p orbitals, while the conduction band minimum is a result of both the cation's s orbital and O-2p orbitals. Conversely, in GaPS₄, InPS₄ and Tl₃PS₄, the valence band maximum is dominated by the p orbitals of sulfur atoms, with the porbitals of phosphorus atoms in the [PS₄]^3- groups showing increase activity in the conduction band. The dielectric function analysis reveals that the peak values for both [PO₄]^3- and [PS₄]^3- compounds experience a redshift with the enlargement of the cation size, with the [PS₄]^3- compounds exhibiting a larger static dielectric constant compared to their [PO₄]^3- counterparts. Birefringence calculations at 1 064 nm show that GaPS₄ has the highest birefringence value (0.247), attributed to the sensitivity of its internal P—S bonds and Ga atoms to energy changes. The other compounds exhibit birefringence values of 0.017 (GaPO₄), 0.049 (InPO₄), 0.057 (TlPO₄), 0.022 (InPS₄), and 0.038 (Tl₃PS₄). Differential charge density and population analysis suggest that the optical effects and band structures of these six compounds are predominantly influenced by the [PO₄]^3- and [PS₄]^3- groups. Elastic modulus analysis concludes that the phosphates exhibit superior elastic properties over the thiophosphates, with indium-containing compounds showing enhanced mechanical stability and rigidity.