This work deals with the synthesis and crystal structure study of new bismuth oxo-arsenates and their oxo-phosphates homologous: Bi₆ZnO₇(AsO₄)₂ vs Bi₆ZnO₇(PO₄)₂ and Bi_3.667Cd₃O₄(AsO₄)₃ vs Bi₃Cd₄O₄(PO₄)₃. Their crystal structures were solved using single crystal X-Ray Diffraction. These are two other examples of crystal structures built on ribbon-like polycations formed of the linkage of oxo-centered O(Bi,M)₄ tetrahedra sharing edges and surrounded by isolated XO₄ groups (X= As or P), where the O(Bi,M)₄ units are derived from the fluorite topology structure. Dealing with Bi₆ZnO₇(PO₄), its acentric space group was confirmed by preliminary second harmonic generation (SHG). The P/As substitution led to a centrosymmetric space group due to local reorientation of oxo-anions. This is strongly related to steric effects between AsO₄ (d As-O= 1.6-1.7Ã…) and PO₄ (d P-O= 1.4-1.5Ã…). Concerning Bi_3.667Cd₃O₄(AsO₄)₃ and Bi₃Cd₄O₄(PO₄)₃, they show a second example of the reorientation of the XO₄ groups depending of the X chemical nature. Finally, we present an original topology of oxo-centered units obtained with Bi₅KO₅(AsO₄). The photoluminescence properties of Bi₅KO₅(AsO₄) and Bi₆ZnO₇(AsO₄)₂ were also investigated. The first one emits at room temperature in the reddish-orange range (single band peak at 615nm assigned to the Bⁱ³⁺: ³P₁→¹S₀ transition whereas the second exhibits a weak emission in the green range (peak at 530nm). Its intriguing temperature dependence is discussed in the paper.