We report a careful and systematic study of thermal and photochemical degradation of a series of complex haloplumbates APbX3 (X = I, Br) with hybrid organic (A+ = CH3NH3) and inorganic (A+ = Cs+) cations under anoxic conditions (i.e., without exposure to oxygen and moisture by testing in an inert glovebox environment). We show that the most common hybrid materials (e.g., MAPbI3) are intrinsically unstable with respect to the heat- and light-induced stress and, therefore, can hardly sustain the real solar cell operation conditions. On the contrary, the cesium-based all-inorganic complex lead halides revealed far superior stability and, therefore, provide an impetus for creation of highly efficient and stable perovskite solar cells that can potentially achieve pragmatic operational benchmarks.