Density functional theory (DFT) calculations using sixteen different approaches, fourteen of which were designed to include dispersion interactions [DFT + D and van der Waals (vdW)-DF methods], were performed for a set of sixteen framework compounds with either SiO2 or AlPO4 composition. The compounds include four dense structures (α-quartz, α-cristobalite, and their AlPO4 analogues), eight all-silica zeolites, and four aluminophosphate zeotypes (AlPOs). We analyzed the performance in reproducing the equilibrium structure for all systems, and computed bulk moduli and relative stabilities were compared to experiments for those compounds where experimental data are available. We found that the results obtained with functionals that take into account dispersive interactions are closer to experiments than those obtained with a bare generalized gradient functional. However, the variation among individual methods is considerable, and functionals that perform well for one quantity may give rather large deviations for another. Taking together the whole body of results, it appears that the Perdew-Burke-Ernzerhof functional including a many-body dispersion correction and the rev-vdW-DF2 methods present the best performance for the description of SiO2 and AlPO4 materials.