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 Bi3.667Cd3O4(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= 1.6-1.7Å) and PO4 (d P-O= 1.4-1.5Å). Concerning Bi3.667Cd3O4(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.